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
Question 1.
Prove that:
Solution.
L.H.S. =
![=\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.](http://s0.wp.com/latex.php?latex=%3D%5Cleft%5B+%7B+%5Cleft%28+%5Cfrac+%7B+1+%7D%7B+2+%7D+%5Cright%29+%7D%5E%7B+2+%7D%2B%7B+%5Cleft%28+%5Cfrac+%7B+1+%7D%7B+2+%7D+%5Cright%29+%7D%5E%7B+2+%7D-%7B+%5Cleft%28+1+%5Cright%29+%7D%5E%7B+2+%7D+%5Cright%5D+%3D%5Cfrac+%7B+1+%7D%7B+4+%7D+%2B%5Cfrac+%7B+1+%7D%7B+4+%7D+-1%3D%5Cfrac+%7B+-1+%7D%7B+2+%7D+%3D%5Cquad+R.H.S.&bg=ffffff&fg=000&s=0 "=\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.
Solution.
L.H.S. =
Question 3.
Solution.
L.H.S. =
Question 4.
Solution.
L.H.S. =
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:
Question 6.
Solution.
We have,
Question 7.
Solution.
We have,
Question 8.
Solution.
We have,
Question 9.
Solution.
We have,
![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](http://s0.wp.com/latex.php?latex=cos%5Cleft%28+%5Cfrac+%7B+3%5Cpi+%7D%7B+2+%7D+%2Bx+%5Cright%29+cos%5Cleft%28+2%5Cpi+%2Bx+%5Cright%29+%5Cleft%5B+cot%5Cleft%28+%5Cfrac+%7B+3%5Cpi+%7D%7B+2+%7D+-x+%5Cright%29+%2Bcot%5Cleft%28+2%5Cpi+%2Bx+%5Cright%29+%5Cright%5D+%3D1&bg=ffffff&fg=000&s=0 "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")
Question 10.
sin(n +1 )x sin(n + 2)x + cos(n +1 )x cos(n + 2)x = cosx
Solution.
We have,
Question 11.
Solution.
We have,
Question 12.
sin26x – sin24x= sin2x sin10x
Solution.
Question 13.
cos22x – cos26x = sin 4x sin 8x
Solution.
Question 14.
sin2x + 2 sin 4x + sin 6x = 4 cos2 x sin 4x
Solution.
We have,
Question 15.
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Solution.
Question 16.
Solution.
We have,
Question 17.
Solution.
We have,
Question 18.
Solution.
Question 19.
Solution.
Question 20.
Solution.
Question 21.
Solution.
Question 22.
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution.
We know that 3x = 2x + x.
Therefore,
Question 23.
Solution.
Question 24.
cos 4x = 1 – 8 sin2x cos2x
Solution.
Question 25.
cos 6x = 32 cos6 x – 48 cos4x + 18 cos2 x -1
Solution.
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.
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