NCERT Solutions For Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3
Here, Below you all know about NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 Question Answer. I know many of you confuse about finding Chapter 3 Trigonometric Functions Ex 3.3 Of Class 11 NCERT Solutions. So, Read the full post below and get your solutions.
Textbook | NCERT |
Board | CBSE |
Category | NCERT Solutions |
Class | Class 10 |
Subject | Maths |
Chapter | Chapter 3 |
Exercise | Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.3 |
Number of Questions Solved | 25 |

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

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.3 PDF
For NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3, you may click on the link below and get your NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise pdf file.
Finally, You all know about NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3. If you have any questions, then comment below and share this post with others.