#### Trigonometry Book Back Questions

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. The degree measure of $\frac{\pi}{8}$ is ______.

(a)

20o60'

(b)

22o30'

(c)

20o60'

(d)

20o30'

2. The value of $\sin(-420^o)$ is _______.

(a)

$\frac{\sqrt3}{2}$

(b)

$-\frac{\sqrt3}{2}$

(c)

$\frac{1}{2}$

(d)

$\frac{-1}{2}$

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

(a)

-1

(b)

cos2 A

(c)

sec2 A

(d)

1

4. The value of cos245o - sin245o is_______.

(a)

$\frac{\sqrt3}{2}$

(b)

$\frac{1}{2}$

(c)

0

(d)

$\frac{1}{\sqrt{2}}$

5. The value of $\frac{2\tan30^o}{1+tan^230}$ is _____.

(a)

$\frac12$

(b)

$\frac{1}{\sqrt3}$

(c)

$\frac{\sqrt{3}}{2}$

(d)

$\sqrt3$

6. 3 x 2 = 6
7. Convert the following degree measure into radian measure 60o

8. Evaluate : $\cos\left[\tan^{-1}\left(\frac34\right)\right]$

9. Find the values of the following  cot 75°

10. 3 x 3 = 9
11. Prove that  $\sec { \left( \frac { 3\pi }{ 2 } -\theta \right) } \sec { \left( \theta -\frac { 5\pi }{ 2 } \right) } +\tan { \left( \frac { 5\pi }{ 2 } +\theta \right) } \tan { \left( \theta -\frac { 5\pi }{ 2 } \right) } =-1$

12. Express each of the following as the sum or difference of sine or cosine : $\sin \frac{A}{8} \sin \frac{3 A}{8}$

13. Prove that $\frac { sin(-\theta )tan({ 90 }^{ o }-\theta )sec\left( { 180 }^{ o }-\theta \right) }{ sin(180+\theta )cot(360-\theta )cosec({ 90 }^{ o }-\theta ) } =1$

14. 2 x 5 = 10
15. If $\sin { A } =\frac { 3 }{ 5 }$ 0 < A < $\frac{\pi}{2}$  and $\cos { B } =\frac { -12 }{ 13 }$ , π < B < $\frac{3\pi}{2}$ find the values of the following $\tan(A-B)$

16. If tan $\alpha={{1}\over{7}},\sin\beta={{1}\over{\sqrt{10}}},$ Prove that $\alpha+2\beta={{\pi}\over{4}}$ where $0<\alpha<{{\pi}\over{2}}$ and $0<\beta<{{\pi}\over{2.}}$