#### Trigonometry Important Questions

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. $\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } }$=

(a)

$\sqrt{2}$

(b)

$\sqrt{3}$

(c)

2

(d)

4

2. If tan400=λ, then $\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } }$=

(a)

$\frac { 1-\lambda ^{ 2 } }{ \lambda }$

(b)

$\frac { 1+{ \lambda }^{ 2 } }{ \lambda }$

(c)

$\frac { 1+{ \lambda }^{ 2 } }{ 2\lambda }$

(d)

$\frac { 1-{ \lambda }^{ 2 } }{ 2\lambda }$

3. $\frac { sin(A-B) }{ cosAcosB } +\frac { sin(B-C) }{ cosBcosC } +\frac { sin(C-A) }{ cosCcosA }$ is

(a)

sinA+sinB+sinC

(b)

1

(c)

0

(d)

cosA+cosB+cosC

4. If tanx=$\frac { -1 }{ \sqrt { 5 } }$ and x lies in the IV quadrant, then the value of cosx is

(a)

$\sqrt { \frac { 5 }{ 6 } }$

(b)

$\frac { 2 }{ \sqrt { 6 } }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 1 }{ \sqrt { 6 } }$

5. Which of the following is incorrect?

(a)

sinx=$\frac { -1 }{ 5 }$

(b)

cosx=1

(c)

secx=$\frac { 1 }{ 2 }$

(d)

tanx=20

6. 6 x 2 = 12
7. Prove that $sinx+sin2x+sin3x=sin2x(1+2cosx)$

8. If a cos (x + y) = b cos (x - y), show that (a + b) tan x = (a - b) cot y.

9. Evaluate sin$\left( \frac { -11\pi }{ 3 } \right)$.

10. Prove that $\frac { cos(2\pi +x)cosec(2\pi +x)tan\left( \frac { \pi }{ 2 } +x \right) }{ sec\left( \frac { \pi }{ 2 } +x \right) cos.cot(\pi +x) }$=1

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

12. Prove that ${ tan }^{ -1 }\left( \frac { 1 }{ 7 } \right) +{ tan }^{ -1 }\left( \frac { 1 }{ 13 } \right) ={ tan }^{ -1 }\frac { 2 }{ 9 }$

13. 6 x 3 = 18
14. Show that $\sin ^{ 2 }{ \frac { \pi }{ 18 } } +\sin ^{ 2 }{ \frac { \pi }{ 9 } } +\sin ^{ 2 }{ \frac { 7\pi }{ 18 } } +\sin ^{ 2 }{ \frac { 4\pi }{ 9 } } =2$

15. If sin A = $\frac{3}{5}$ and cos B = $\frac{9}{41}$, 0 < A < $\frac{\pi}{2}$, 0 < B < $\frac{\pi}{2}$. Find the value of sin (A + B)

16. Find the principal value of $sin^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right)$.

17. Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x.

18. Simplify:$\frac{cos(90°+\theta)sec(-\theta)tan(180°-\theta)}{sec(360°-\theta)sin(180°+\theta)cot(90°+\theta)}$

19. Show that 4 sin A sin (60° +A).sin(60° - A) = sin 3A

20. 3 x 5 = 15
21. if cot $\theta$ (1+sin$\theta$) = 4 m and cot $\theta$ (1 - sin $\theta$) = 4n , prove that (m2 - n2)2 = mn

22. Two trees A and B are on the same side of a river. From a point C in the river the distance of trees A and B are 250 m and 300 m respectively. If the angle C is 45o, find the distance between the trees.

23. Solve $\sin { 2x } +\sin { 4x } +\sin { 6x } =0$