#### Trignometry - Important Question Paper

11th Standard

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Time : 01:00:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. 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)

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

2. The value of 1-2sin245o is

(a)

1

(b)

$\frac{1}{2}$

(c)

$\frac14$

(d)

0

3. The value 4cos340o-3cos40o is

(a)

$\frac{\sqrt3}{2}$

(b)

$\frac{-1}{2}$

(c)

$\frac{1}{2}$

(d)

$\frac{1}{\sqrt2}$

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

(a)

$\frac12$

(b)

$\frac{1}{\sqrt3}$

(c)

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

(d)

$\sqrt3$

5. If $\sin A=\frac{1}{2}$ then $4\cos^3A-3\cos A$ is

(a)

1

(b)

0

(c)

$\frac{\sqrt3}{2}$

(d)

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

6. 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)

$\frac{1}{\sqrt2}$

7. $\sin\left(\cos^{-1}\frac{3}{5}\right)$ is

(a)

$\frac{3}{5}$

(b)

$\frac{5}{3}$

(c)

$\frac{4}{5}$

(d)

$\frac{5}{4}$

8. The value of $\frac{1}{cosec(-45^o)}$ is

(a)

$\frac{-1}{\sqrt2}$

(b)

$\frac{1}{\sqrt2}$

(c)

$\sqrt2$

(d)

$-\sqrt2$

9. If p sec 50o=tan 50o then p is

(a)

cos 50o

(b)

sin 50o

(c)

tan 50o

(d)

sec 50o

10. $\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}$ is

(a)

cos2x-sin2x

(b)

sin2x-cos2x

(c)

1

(d)

0

11. Part B

6 x 2 = 12
12. Solve: $\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$

13. Determine the quadrants in which the following degree lie. 1195°

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

15. Find the values of the following trigonometric ratios. $\sec { \left( { 390 }^{ o } \right) }$

16. Find the values of the following trigonometric ratios. $\tan { \left( { -855 }^{ o } \right) }$

17. Find the values of each of the following trigonometric ratios.  $cosec { \left( { 1125 }^{ o } \right) }$

18. Part C

6 x 3 = 18
19. If $\sin A=\frac35$ where $0<A<\frac { \pi }{ 2 }$ and $cosB=\frac { -12 }{ 13 } ,\pi <A<\frac { 3\pi }{ 2 }$ find the value of
$\tan(A-B)$

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

21. If $\cos { A } =\frac { 13 }{ 14 } \quad$and $\cos { B } =\frac { 1 }{ 7 }$ where A, B are acute angles, prove that A-B=$\frac { \pi }{ 3 }$

22. Prove that 2 tan 80° = tan 85° - tan 5°.

23. If A+B=45° , Prove that (1 + tan A) (1+ tan B) = 2 and hence deduce the value of $\tan { 22{ \frac { 1 }{ 2 } }^{ ° } }$

24. Find all other trigonometrical ratios if $\sin x=\frac{-2\sqrt6}{5}$ and x lies in III quadrant?

25. Part D

2 x 5 = 10
26. Prove that sin(n+1)x sin(n+2) x+cos(n+1)xcos(n+2)x=cosx.

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