NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3.

Board	CBSE
Textbook	NCERT
Class	Class 11
Subject	Maths
Chapter	Chapter 3
Chapter Name	Trigonometric Functions
Exercise	Ex 3.3
Number of Questions Solved	25
Category	NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3

Question 1.
Prove that: ${ sin }^{ 2 }\frac { \pi }{ 6 } +{ cos }^{ 2 }\frac { \pi }{ 3 } -{ tan }^{ 2 }\frac { \pi }{ 4 } =-\frac { 1 }{ 2 }$
Solution.
L.H.S. = ${ sin }^{ 2 }\frac { \pi }{ 6 } +{ cos }^{ 2 }\frac { \pi }{ 3 } -{ tan }^{ 2 }\frac { \pi }{ 4 } =-\frac { 1 }{ 2 }$
$=\left[ { \left( \frac { 1 }{ 2 } \right) }^{ 2 }+{ \left( \frac { 1 }{ 2 } \right) }^{ 2 }-{ \left( 1 \right) }^{ 2 } \right] =\frac { 1 }{ 4 } +\frac { 1 }{ 4 } -1=\frac { -1 }{ 2 } =\quad R.H.S.$

Question 2.
$2{ sin }^{ 2 }\frac { \pi }{ 6 } +{ cosec }^{ 2 }\frac { 7\pi }{ 6 } { cos }^{ 2 }\frac { \pi }{ 3 } =\frac { 3 }{ 2 }$
Solution.
L.H.S. = $2{ sin }^{ 2 }\frac { \pi }{ 6 } +{ cosec }^{ 2 }\frac { 7\pi }{ 6 } { cos }^{ 2 }\frac { \pi }{ 3 }$
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 1

Question 3.
${ cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 } =6$
Solution.
L.H.S. = ${ cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 }$
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 2

Question 4.
$2{ sin }^{ 2 }\frac { 3\pi }{ 4 } +2{ cos }^{ 2 }\frac { \pi }{ 4 } +2{ sec }^{ 2 }\frac { \pi }{ 3 } =10$
Solution.
L.H.S. = $2{ sin }^{ 2 }\frac { 3\pi }{ 4 } +2{ cos }^{ 2 }\frac { \pi }{ 4 } +2{ sec }^{ 2 }\frac { \pi }{ 3 }$
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 3

Question 5.
Find the value of:
(i) sin 75°
(ii) tan 15°
Solution.
(i) sin (75°) = sin (30° + 45°)
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 4

(ii) tan 15° = tan (45° – 30°)
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 5

Prove the following:
Question 6.
$cos\left( \frac { \pi }{ 4 } -x \right) cos\left( \frac { \pi }{ 4 } -y \right) -sin\left( \frac { \pi }{ 4 } -x \right) sin\left( \frac { \pi }{ 4 } -y \right)$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 7

Question 7.
$\frac { tan\left( \frac { \pi }{ 4 } +x \right) }{ tan\left( \frac { \pi }{ 4 } -x \right) } ={ \left( \frac { 1+tan\quad x }{ 1-tan\quad x } \right) }^{ 2 }$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 8

Question 8.
$\frac { cos\left( \pi +x \right) cos\left( -x \right) }{ sin\left( \pi -x \right) cos\left( \frac { \pi }{ 2 } +x \right) } ={ cot }^{ 2 }x$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 9

Question 9.
$cos\left( \frac { 3\pi }{ 2 } +x \right) cos\left( 2\pi +x \right) \left[ cot\left( \frac { 3\pi }{ 2 } -x \right) +cot\left( 2\pi +x \right) \right] =1$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 10

Question 10.
sin(n +1 )x sin(n + 2)x + cos(n +1 )x cos(n + 2)x = cosx
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 11

Question 11.
$cos\left( \frac { 3\pi }{ 4 } +x \right) -cos\left( \frac { 3\pi }{ 4 } -x \right) =-\sqrt { 2 } sinx$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 12

Question 12.
sin²6x – sin²4x= sin²x sin10x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 14

Question 13.
cos²2x – cos²6x = sin 4x sin 8x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 15

Question 14.
sin2x + 2 sin 4x + sin 6x = 4 cos² x sin 4x
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 16

Question 15.
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 17

Question 16.
$\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x }$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 18

Question 17.
$\frac { sin5x+sin3x }{ cos5x+cos3x } =tan4x$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 19

Question 18.
$\frac { sinx-siny }{ cosx+cosy } =tan\left( \frac { x-y }{ 2 } \right)$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 20

Question 19.
$\frac { sinx+sin3x }{ cosx+cos3x } =tan2x$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 22

Question 20.
$\frac { sinx-sin3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } =2sinx$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 23

Question 21.
$\frac { cos4x+cos3x+cos2x }{ sin4x+sin3x+sin2x } =cot3x$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 24

Question 22.
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution.
We know that 3x = 2x + x.
Therefore,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 25

Question 23.
$tan4x=\frac { 4tanx\left( 1-{ tan }^{ 2 }x \right) }{ 1-6{ tan }^{ 2 }x+{ tan }^{ 4 }x }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 26

Question 24.
cos 4x = 1 – 8 sin²x cos²x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 27

Question 25.
cos 6x = 32 cos6 x – 48 cos⁴x + 18 cos² x -1
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 28

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3

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