**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:**

**Question 2.**

If (1 + cos A) (1 – cos A) =3/4, find the value of sec A.

**Solution:**

**Question 3.**

If cosec θ + cot θ = x, find the value of cosec θ – cot θ

**Solution:**

**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:**

**Short Answer Type Questions II [3 Marks]**

**Question 5.**

Given tan A = 5/12 , find the other trigonometric ratios of the angle A.

**Solution:**

**Question 6.**

Prove that 1/sec A – tan A-1/cosA=1/ cos A -1/sec A + tan A

**Solution:**

**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:**

**Long Answer Type Questions [4 Marks]**

**Question 8.**

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

- tan A + cot B
- sec A – cosec B

**Solution:**

**Question 9.**

If sec A = x + 1/4x, prove that sec A + tan A = 2x or 1/2x

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

**Solution:**

**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:**

**2015**

**Very Short Answer Type Questions [1 Mark]**

**Question 13.**

Evaluate: sin θ.sec(9O – θ)

**Solution:**

**Question 14.**

Find the value of (cosec² θ – l).tan²θ

**Solution:**

**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:**

**Short Answer Type Questions II [3 Marks]**

**Question 16.**

If 7sin²A + 3cos²A = 4, show that tan A =1/√3

**Solution:**

**Question 17.**

For any acute angle θ, prove that

- sin²θ + cos²θ = 1
- 1 + cot²θ = cosec²θ

**Solution:**

**Long Answer Type Questions[4 Marks]**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:**

**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:**

**Question 21.**

If cosec θ = 5/3, then what is the value of cos θ + tanθ

**Solution:**

**Question 22.**

Find the value of tan(65° – θ) – cot(25° + θ)

**Solution:**

**Question 23.**

Find the value of sin 38° – cos 52°.

**Solution:**

**Question 24.**

Find the value of cos θ + sec θ, when it is given that cos θ =1/2

**Solution:**

**Question 25.**

Evaluate: 3 cot² 60° + sec² 45°.

**Solution:**

**Short Answer Type Questions I [2 Marks]**

**Question 26.**

Solve the equation for θ: cos²θ/cot²θ – cos² θ=3

**Solution:**

**Question 27.**

Express cos A in terms of cot A.

**Solution:**

**Question 28.**

If A, B, and C are the interior angles of a ΔABC, show that tan(A+B/2)=cot C/2

**Solution:**

**Short Answer Type Questions II [3 Marks]**

**Question 29.**

If sin A = cos A, find the value of 2tan²A + sin²A + 1.

**Solution:**

**Question 30.**

If tan θ + cot θ= 2, find the value of √tan²θ + cot²θ.

**Solution:**

**Question 31.**

If tan(A – B) = 1/√3 and tan (A + B) = √3, find A and B.

**Solution:**

**Question 32.**

If ac = r cos θ. sin Φ; y = r sinθ. sinΦ; z = r cos Φ. Prove that x² + y² + z²= r².

**Solution:**

**Question 33.**

**Solution:**

**Question 34.**

**Solution:**

**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.

- Taking A = 60°, B = 45° and
- Taking A = 45°, B = 30°

**Solution:**

**Question 36.**

If cosec A + cot A = m, show that m²-1/ m² + 1= cos A.

**Solution:**

**Question 37.**

Prove that: (sec θ + tan θ)² = cosec θ +1/cosec θ -1

**Solution:**

**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:**

**Question 39.**

**Solution:**

**Question 40.**

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

- sin²P
- cos²R and tan R
- sin P x cos P
- sin²P – cos²P

**Solution:**

**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:**

**Short Answer Type Questions II [3 Marks]**

**Question 42.**

If sin A = cos A, find the value of 2tan² A + sin² A – 1

**Solution:**

**Question 43.**

Show that cosec² θ – tan²(90° – θ) = sin² θ + sin² (90° – θ).

**Solution:**

**Question 44.**

ABC is a triangle right angled at C and AC = √3 BC. Prove that ∠ABC=60°

**Solution:**

**Question 45.**

**Solution:**

**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.**

**Solution:**

**Question 48.**

If sec θ + tan θ = p, then find the value of cosecθ

**Solution:**

**Question 49.**

Evaluate: 4/Cot² 30°+1/sin² 60°-cos² 45°

**Solution:**

**Question 50.**

Evaluate: 4(sin430° + cos460°) – 3(cos²45°-sin²90°)

**Solution:**

**Question 51.**

Prove that 1/cosecA+cotA-1/sinA=1/sinA-1/cosecA-cotA

**Solution:**

**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:**

**Question 53.**

If sin A = √3/2, find the value of 2 cot² A -1.

**Solution:**

**Short Answer Type Questions II [3 Marks]**

**Question 54.**

**Solution:**

**Long Answer Type Questions [4 Marks]**

**Question 55.**

**Solution:**

**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:**

**2011**

**Short Answer Type Questions I [2 Marks]**

**Question 57.**

Prove that: cosA/1+sinA+1+sinA/cosA=2 secA

**Solution:**

**Question 58.**

**Solution:**

**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:**

**Question 60.**

If cosθ-sinθ=√2 sinθ,prove that cosθ+sinθ=√2 cosθ

**Solution:**

**Question 61.**

If cosec (A-B) = 2, cot (A + B) = —0° < (A + B) <90°, A > B, then find A and B

**Solution:**

**Long Answer Type Questions [4 Marks]**

**Question 62.**

**Solution:**

**Question 63.**

**Solution:**

**Question 64.**

Determine the value of x such that 2 cosec² 30° + x sin² 60° -3/4 tan² 30° = 10.

**Solution:**

**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:**

**Question 66.**

If 2r = sec A and 2/x = tan A, find the value of 2(x²-1/x²)

**Solution:**

**Question 67.**

If cosecθ = 2x and cot θ= 2/x, find the value of 2(x²-1/x²)

**Solution:**

**Question 68.**

If 5x = secθ and 5/x = tanθ, find the value of 5(x²-1/x²)

**Solution:**

**Question 69.**

If 7x = cosecθ and 7/x = cot θ, find the value of (x²-1/x²)

**Solution:**

**Question 70.**

If 6x = sec θ and 6/x = tanθ, find the value of 9(x²-1/x²)

**Solution:**

**Question 71.**

If 8r = cosec A and 8/x = cot A, find the value of 4(x²-1/x²)

**Solution:**

**Question 72.**

If 4x = sec θ and 4/x = tan θ, find the value of 8(x²-1/x²)

**Solution:**

**Short Answer Type Questions I [2 Marks]**

**Question 73.**

Find the value of cosec 30° geometrically.

**Solution:**

**Question 74.**

Find the value of sec 60° geometrically

**Solution:**

**Question 75.**

Find the value of sec 45° geometrically

**Solution:**

**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:**

**Question 77.**

Prove that: (1 + cot A – cosec A) (1 + tan A + sec A) = 2.

**Solution:**

**Question 78.**

Prove that: sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ.

**Solution:**

**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:**

**Question 80.**

If sec2 θ(1 + sin θ) (1 – sin θ) = k, then find the value of k.

**Solution:**

**Question 81.**

If sec A = 15/7 and A + B = 90°, find the value of cosec B

**Solution:**

**Short Answer Type Question I [2 Marks]**

**Question 82.**

**Solution:**

**Short Answer Type Questions II [3 Marks]**

**Question 83.**

**Solution:**

**Question 84.**

**Solution:**

**Question 85.**

**Solution:**