#### Trigonometry Model Question Paper

11th Standard

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Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The radian measure of 37o30' is

(a)

$\frac{5\pi}{24}$

(b)

$\frac{3\pi}{24}$

(c)

$\frac{7\pi}{24}$

(d)

$\frac{9\pi}{24}$

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 cos245o-sin245o is

(a)

$\frac{\sqrt3}{2}$

(b)

$\frac{1}{2}$

(c)

0

(d)

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

4. The value of $\frac{3\tan10^o-\tan^310}{1-3\tan^210}$ is

(a)

$\frac{1}{\sqrt3}$

(b)

$\frac{1}{2}$

(c)

$\frac{\sqrt3}2$

(d)

$\frac{1}{\sqrt2}$

5. If $\alpha$ and $\beta$ be between 0 and $\frac{\pi}{2}$ and if $\cos(\alpha+\beta)=\frac{12}{13}$ and $\sin(\alpha-\beta)=\frac{3}{5}$ then $\sin2\alpha$ is

(a)

$\frac{16}{15}$

(b)

0

(c)

$\frac{56}{65}$

(d)

$\frac{64}{65}$

6. 5 x 2 = 10
7. Prove that $\tan^{-1}\left(\frac{4}{3}\right)-\tan^{-1}\left(\frac{1}{7}\right)=\frac{\pi}{4}$

8. Convert the following degree measure into radian measure 150o

9. Find the values of the following trigonometric ratios. $\sin { { 300 }^{ o } }$

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

11. Evaluate$\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]$

12. 5 x 3 = 15
13. Prove that  $2\sin ^{ 2 }{ \frac { \pi }{ 6 } } +\ cosec ^{ 2 }{ \frac { 7\pi }{ 6 } } \cos ^{ 2 }{ \frac { \pi }{ 3 } } =\frac { 3 }{ 2 }$

14. Prove that: $\cos { { 510 }^{ o } } \cos { { 330 }^{ o } } +\sin { { 390 }^{ o } } \cos { { 120 }^{ o } } =-1$

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

16. Prove that $\frac{\sin5x+\sin3x}{\cos5x+\cos3x}=\tan4x$

17. If tan(x + y) = 42 and x = tan–1(2), then find y

18. 4 x 5 = 20
19. If $\cos(\alpha+\beta)=\frac45$ and $\sin(\alpha-\beta)=\frac{5}{13}$ where $(\alpha+\beta)$ and $(\alpha-\beta)$ are acute, then find $\tan2\alpha$

20. 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 sin (A - B)

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

22. Prove that cos 4x = 1 - 8 sin2x cos2x.