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.

• Trigonometric Functions Class 11 Ex 3.1
• Trigonometric Functions Class 11 Ex 3.2
• Trigonometric Functions Class 11 Ex 3.4

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

Ex 3.3 Class 11 Maths 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. = \({ sin }^{ 2 }\frac { \pi }{ 6 } +{ cos }^{ 2 }\frac { \pi }{ 3 } -{ tan }^{ 2 }\frac { \pi }{ 4 } =-\frac { 1 }{ 2 } \)
\(=\left[ { \left( \frac { 1 }{ 2 } \right) }^{ 2 }+{ \left( \frac { 1 }{ 2 } \right) }^{ 2 }-{ \left( 1 \right) }^{ 2 } \right] =\frac { 1 }{ 4 } +\frac { 1 }{ 4 } -1=\frac { -1 }{ 2 } =\quad R.H.S.\)

Ex 3.3 Class 11 Maths 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. = \(2{ sin }^{ 2 }\frac { \pi }{ 6 } +{ cosec }^{ 2 }\frac { 7\pi }{ 6 } { cos }^{ 2 }\frac { \pi }{ 3 } \)

Ex 3.3 Class 11 Maths Question 3.
\({ cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 } =6\)
Solution.
L.H.S. = \({ cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 } \)

Ex 3.3 Class 11 Maths 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. = \(2{ sin }^{ 2 }\frac { 3\pi }{ 4 } +2{ cos }^{ 2 }\frac { \pi }{ 4 } +2{ sec }^{ 2 }\frac { \pi }{ 3 } \)

Ex 3.3 Class 11 Maths Question 5.
Find the value of:
(i) sin 75°
(ii) tan 15°
Solution.
(i) sin (75°) = sin (30° + 45°)

(ii) tan 15° = tan (45° – 30°)

Prove the following:
Ex 3.3 Class 11 Maths 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,

Ex 3.3 Class 11 Maths 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,

Ex 3.3 Class 11 Maths 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,

Ex 3.3 Class 11 Maths 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,

Ex 3.3 Class 11 Maths Question 10.
sin(n +1 )x sin(n + 2)x + cos(n +1 )x cos(n + 2)x = cosx
Solution.
We have,

Ex 3.3 Class 11 Maths Question 11.
\(cos\left( \frac { 3\pi }{ 4 } +x \right) -cos\left( \frac { 3\pi }{ 4 } -x \right) =-\sqrt { 2 } sinx\)
Solution.
We have,

Ex 3.3 Class 11 Maths Question 12.
sin²6x – sin²4x= sin²x sin10x
Solution.

Ex 3.3 Class 11 Maths Question 13.
cos²2x – cos²6x = sin 4x sin 8x
Solution.

Ex 3.3 Class 11 Maths Question 14.
sin2x + 2 sin 4x + sin 6x = 4 cos² x sin 4x
Solution.
We have,

Ex 3.3 Class 11 Maths Question 15.
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Solution.

Ex 3.3 Class 11 Maths Question 16.
\( \frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x } \)
Solution.
We have,

Ex 3.3 Class 11 Maths Question 17.
\(\frac { sin5x+sin3x }{ cos5x+cos3x } =tan4x\)
Solution.
We have,

Ex 3.3 Class 11 Maths Question 18.
\(\frac { sinx-siny }{ cosx+cosy } =tan\left( \frac { x-y }{ 2 } \right) \)
Solution.

Ex 3.3 Class 11 Maths Question 19.
\(\frac { sinx+sin3x }{ cosx+cos3x } =tan2x\)
Solution.

Ex 3.3 Class 11 Maths Question 20.
\(\frac { sinx-sin3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } =2sinx\)
Solution.

Ex 3.3 Class 11 Maths Question 21.
\(\frac { cos4x+cos3x+cos2x }{ sin4x+sin3x+sin2x } =cot3x\)
Solution.

Ex 3.3 Class 11 Maths Question 22.
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution.
We know that 3x = 2x + x.
Therefore,

Ex 3.3 Class 11 Maths Question 23.
\(tan4x=\frac { 4tanx\left( 1-{ tan }^{ 2 }x \right) }{ 1-6{ tan }^{ 2 }x+{ tan }^{ 4 }x } \)
Solution.

Ex 3.3 Class 11 Maths Question 24.
cos 4x = 1 – 8 sin²x cos²x
Solution.

Ex 3.3 Class 11 Maths Question 25.
cos 6x = 32 cos6 x – 48 cos⁴x + 18 cos² x -1
Solution.

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