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Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions

Important Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry with solutions includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 8 Introduction to Trigonometry.

Important Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry

Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 8 Introduction to Trigonometry.

2016

Very Short Answer Type Questions [1 Mark]

Question 1.
Find the value of sec² 42° – cosec² 48°.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 1

Question 2.
If (1 + cos A) (1 – cos A) =3/4, find the value of sec A.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 2

Question 3.
If cosec θ + cot θ = x, find the value of cosec θ – cot θ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 3

Short Answer Type Question I [2 Marks]

Question 4.
Write the values of sec 0°, sec 30°, sec 45°, sec 60° and sec 90°. What happens to sec x when x increases from 0° to 90° ?
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 4

Short Answer Type Questions II [3 Marks]

Question 5.
Given tan A = 5/12 , find the other trigonometric ratios of the angle A.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 5

Question 6.
Prove that 1/sec A – tan A-1/cosA=1/ cos A -1/sec A + tan A
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 6

Question 7.
If sin θ = 12/13, 0° < θ < 90°, find the value of: sin² θ- cos² θ /2 sin θ. cos θ  x 1/tan² θ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 7

Long Answer Type Questions [4 Marks]

Question 8.
If sin (A + B) = 1 and tan (A – B) = 1/√3, find the value of:

  1. tan A + cot B
  2. sec A – cosec B

Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 8

Question 9.
If sec A = x + 1/4x, prove that sec A + tan A = 2x or 1/2x
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 9

Question 10.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 10
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 11

Question 11.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 12
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 13

Question 12.
If sec θ – tan θ = x, show that: sec θ=1/2(x+1/x) and tan θ=1/2(1/x-x)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 14

2015

Very Short Answer Type Questions [1 Mark]

Question 13.
Evaluate: sin θ.sec(9O – θ)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 15

Question 14.
Find the value of (cosec² θ – l).tan²θ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 16

Short Answer Type Question I [2 Marks]

Question 15.
Prove the following identity:sin³ θ+cos³ θ/sin θ+cos θ= 1 – sin θ.cos θ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 17

Short Answer Type Questions II [3 Marks]

Question 16.
If 7sin²A + 3cos²A = 4, show that tan A =1/√3
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 18

Question 17.
For any acute angle θ, prove that

  1. sin²θ + cos²θ = 1
  2. 1 + cot²θ = cosec²θ

Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 19

Long Answer Type Questions[4 Marks]

Question 18.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 20
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 21

Question 19.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 22
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 23

2014

Very Short Answer Type Questions [1 Mark]

Question 20.
If sinθ = x and sec θ = y then find the value of cot θ.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 24

Question 21.
If cosec θ = 5/3, then what is the value of cos θ + tanθ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 27
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 28

Question 22.
Find the value of tan(65° – θ) – cot(25° + θ)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 29

Question 23.
Find the value of sin 38° – cos 52°.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 30

Question 24.
Find the value of cos θ + sec θ, when it is given that cos θ =1/2
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 31

Question 25.
Evaluate: 3 cot² 60° + sec² 45°.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 32

Short Answer Type Questions I [2 Marks]

Question 26.
Solve the equation for θ: cos²θ/cot²θ – cos² θ=3
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 33

Question 27.
Express cos A in terms of cot A.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 34

Question 28.
If A, B, and C are the interior angles of a ΔABC, show that tan(A+B/2)=cot C/2
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 35

Short Answer Type Questions II [3 Marks]

Question 29.
If sin A = cos A, find the value of 2tan²A + sin²A + 1.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 36

Question 30.
If tan θ + cot θ= 2, find the value of √tan²θ + cot²θ.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 37

Question 31.
If tan(A – B) = 1/√3 and tan (A + B) = √3, find A and B.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 38

Question 32.
If ac = r cos θ. sin Φ; y = r sinθ. sinΦ; z = r cos Φ. Prove that x² + y² + z²= r².
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 39

Question 33.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 40
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 41

Question 34.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 42
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 43

Long Answer Type Questions [4 Marks]

Question 35.
Given that cos(A – B) = cos A.cos B + sinA.sinB, find the value of cos 15° in two ways.

  1. Taking A = 60°, B = 45° and
  2. Taking A = 45°, B = 30°

Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 44
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 45

Question 36.
If cosec A + cot A = m, show that m²-1/ m² + 1= cos A.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 46

Question 37.
Prove that: (sec θ + tan θ)² = cosec θ +1/cosec θ -1
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 47

Question 38.
If cosec θ + cot θ = q, show that cosec θ – cot θ = 1/q and hence find the values of sin θ and sec θ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 48
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 49

Question 39.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 50
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 51

Question 40.
ΔRPQ is a right angled at Q. If PQ = 5 cm and RQ = 10 cm, find:

  1. sin²P
  2. cos²R and tan R
  3. sin P x cos P
  4. sin²P – cos²P
    Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 52

Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 53

2013

Short Answer Type Question I [2 Marks]

Question 41.
If cos θ + sin θ =√2 cos θ, show that cos θ – sin θ = √2 sin θ.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 54

Short Answer Type Questions II [3 Marks]

Question 42.
If sin A = cos A, find the value of 2tan² A + sin² A – 1
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 55

Question 43.
Show that cosec² θ – tan²(90° – θ) = sin² θ + sin² (90° – θ).
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 56

Question 44.
ABC is a triangle right angled at C and AC = √3 BC. Prove that ∠ABC=60°
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 57

Question 45.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 58
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 59

Question 46.
If tan(A – B) = 1/√3 and tan (A + B) = √3, find A and B
Solution:
Refer to sol of Question no. 19.

Long Answer Type Questions [4 Marks]

Question 47.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 60
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 61

Question 48.
If sec θ + tan θ = p, then find the value of cosecθ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 62

Question 49.
Evaluate: 4/Cot² 30°+1/sin² 60°-cos² 45°
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 63

Question 50.
Evaluate: 4(sin430° + cos460°) – 3(cos²45°-sin²90°)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 64

Question 51.
Prove that 1/cosecA+cotA-1/sinA=1/sinA-1/cosecA-cotA
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 65

2012

Short Answer Type Questions I [2 Marks]

Question 52.
If √3 sin θ – cos θ = 0 and 0° < θ < 90°, find the value of θ.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 66

Question 53.
If sin A = √3/2, find the value of 2 cot² A -1.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 67

Short Answer Type Questions II [3 Marks]

Question 54.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 68
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 69

Long Answer Type Questions [4 Marks]

Question 55.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 70
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 71

Question 56.
In an acute angled triangle ABC, if sin (A + B – C) = 1/2 and cos (B + C – A) = 1/√2 find ∠A, ∠B and ∠C
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 72
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 73

2011

Short Answer Type Questions I [2 Marks]

Question 57.
Prove that: cosA/1+sinA+1+sinA/cosA=2 secA
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 74

Question 58.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 75
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 76

Short Answer Type Questions II [3 Marks]

Question 59.
In the figure below, ΔABC is right angled at B, BC = 7 cm and AC – AB = 1 cm. Find the value of cos A + sin A
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 77
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 78

Question 60.
If cosθ-sinθ=√2 sinθ,prove that cosθ+sinθ=√2 cosθ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 79

Question 61.
If cosec (A-B) = 2, cot (A + B) = —0° < (A + B) <90°, A > B, then find A and B
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 80

Long Answer Type Questions [4 Marks]

Question 62.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 81
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 82

Question 63.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 83
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 84

Question 64.
Determine the value of x such that 2 cosec² 30° + x sin² 60° -3/4 tan² 30° = 10.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 85

2010

Very Short Answer Type Questions [1 Mark]

Question 65.
If 3x= cosec θ and  3/x= cot θ, find the value of 3(x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 86

Question 66.
If 2r = sec A and 2/x = tan A, find the value of 2(x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 87
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 88

Question 67.
If cosecθ = 2x and cot θ= 2/x, find the value of 2(x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 89

Question 68.
If 5x = secθ and 5/x = tanθ, find the value of 5(x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 90

Question 69.
If 7x = cosecθ and 7/x = cot θ, find the value of (x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 91

Question 70.
If 6x = sec θ and 6/x = tanθ, find the value of 9(x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 92

Question 71.
If 8r = cosec A and 8/x = cot A, find the value of 4(x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 93

Question 72.
If 4x = sec θ and 4/x = tan θ, find the value of 8(x²-1/x²)
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 94

Short Answer Type Questions I [2 Marks]

Question 73.
Find the value of cosec 30° geometrically.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 95

Question 74.
Find the value of sec 60° geometrically
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 96
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 97

Question 75.
Find the value of sec 45° geometrically
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 98

Short Answer Type Questions II [3 Marks]

Question 76.
Prove that: (cosec θ – sin θ). (sec θ – cos θ) =1/tan θ+cot θ
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 99

Question 77.
Prove that: (1 + cot A – cosec A) (1 + tan A + sec A) = 2.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 100

Question 78.
Prove that: sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 101

2009

Very Short Answer Type Questions [1 Mark]

Question 79.
If sin θ = 1/3, then find the value of (2 cot² θ + 2).
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 102

Question 80.
If sec2 θ(1 + sin θ) (1 – sin θ) = k, then find the value of k.
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 103

Question 81.
If sec A = 15/7 and A + B = 90°, find the value of cosec B
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 104

Short Answer Type Question I [2 Marks]

Question 82.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 105
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 106

Short Answer Type Questions II [3 Marks]

Question 83.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 107
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 108

Question 84.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 109
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 110

Question 85.
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 111
Solution:
Introduction to Trigonometry Class 10 Maths CBSE Important Questions With Solutions 112

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