Advertisements
|

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.

TextbookNCERT
BoardCBSE
CategoryNCERT Solutions
ClassClass 10
SubjectMaths
ChapterChapter 3
ExerciseClass 11 Maths Chapter 3 Trigonometric Functions Exercise 3.3
Number of Questions Solved25
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

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.

CLICK HERE

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.

Other Chapter of Class 11 Maths Chapter 3 Trigonometric Functions

Similar Posts

Leave a Reply

Your email address will not be published. Required fields are marked *