#### Trigonometry Sample Questions

11th Standard

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Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The degree measure of $\frac{\pi}{8}$ is ______.

(a)

20o60'

(b)

22o30'

(c)

20o60'

(d)

20o30'

2. If $\tan\theta=\frac{1}{\sqrt5}$ and $\theta$ lies in the first quadrant, then $\cos\theta$ is _______.

(a)

$\frac{1}{\sqrt6}$

(b)

$\frac{-1}{\sqrt6}$

(c)

$\frac{\sqrt5}{\sqrt6}$

(d)

$\frac{-\sqrt5}{\sqrt6}$

3. The value of sin 15o cos 15o is ______.

(a)

1

(b)

$\frac{1}{2}$

(c)

$\frac{\sqrt3}{2}$

(d)

$\frac{1}{4}$

4. The value of sec A sin(270o + A) is ______.

(a)

-1

(b)

cos2 A

(c)

sec2 A

(d)

1

5. If sin A + cos A = 1, then sin 2A is equal to _______.

(a)

1

(b)

2

(c)

0

(d)

$\frac{1}{2}$

6. 5 x 2 = 10
7. Find the principal value of the following $\sin ^{-1}\left(-\frac{1}{2}\right)$

8. Find the principal value of the following cosec-1(2)

9. Determine the quadrants in which the following degree lie. -140°

10. Find the value of $\cos\left(\frac{5\pi}{12}\right)$

11. Prove that $sin^2\left(\frac{\pi}{8}+\frac x2\right)-sin^2\left(\frac{\pi}{8}-\frac x2\right)=\frac{1}{\sqrt2}\sin x.$

12. 5 x 3 = 15
13. Prove that $\sqrt3$ cosec 20o- sec 20o = 4

14. Prove that  $2\sin ^{ 2 }{ \frac { \pi }{ 6 } } +\ cosec ^{ 2 }{ \frac { 7\pi }{ 6 } } \cos ^{ 2 }{ \frac { \pi }{ 3 } } =\frac { 3 }{ 2 }$

15. Prove that:  $\sin { \theta } \cos { \theta } \left\{ \sin { \left( \frac { \pi }{ 2 } -\theta \right) } \csc { \theta } +\cos { \left( \frac { \pi }{ 2 } -\theta \right) \sec { \theta } } \right\} =1$

16. If $\alpha$ and $\beta$ are acute angles such that $\tan\alpha=\frac{m}{m+1}$ and $\tan\beta=\frac{1}{2m+1}$, prove that $\alpha+\beta=\frac{\pi}{4}$

17. Show that $\tan\left(\frac{\pi}{3}+x\right)\tan\left(\frac{\pi}{3}-x\right)=\frac{2\cos2x+1}{2\cos2x-1}$

18. 4 x 5 = 20
19. Prove that  $\frac { \sin { \left( { 180 }^{ o }+A \right) \cos { \left( { 90 }^{ o }-A \right) \tan { \left( { 270 }^{ o }-A \right) } } } \quad \quad }{ \sec { \left( { 540 }^{ o }-A \right) \cos { \left( { 360 }^{ o }+A \right) \ cosec { \left( { 270 }^{ o }+A \right) } } } } =-\sin { A } \cos ^{ 2 }{ A }$

20. If $\sin { A } =\frac { 3 }{ 5 }$ 0$\frac{\pi}{2}$  and $\cos { B } =\frac { -12 }{ 13 }$ , π$\frac{3\pi}{2}$ find the values of the following sin (A - B)

21. Prove that cos22x - cos26x = sin 4x.sin 8x

22. Prove that cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1.