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#### Trigonometry Model Question Paper

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. cos10+cos20+cos30+: : :+cos1790=

(a)

0

(b)

1

(c)

-1

(d)

89

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 tanA=$\frac { a }{ a+1 }$ and B=$\frac { 1 }{ 2a+1 }$ then the value of A+B is

(a)

0

(b)

$\frac { \pi }{ 2 }$

(c)

$\frac { \pi }{ 3 }$

(d)

$\frac { \pi }{ 4 }$

5. cosp=$\frac { 1 }{ 7 }$ and cosQ=$\frac { 13 }{ 14 }$ where P,Q are angles, then P-Q is

(a)

$\frac { \pi }{ 6 }$

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 4 }$

(d)

$\frac { 5\pi }{ 12 }$

6. 5 x 2 = 10
7. Find the value of tan $\frac{7\pi}{12}$.

8. Prove that $\sin { \left( \pi +\theta \right) } =-\sin { \theta }$

9. If cosA=$\frac { 4 }{ 5 }$, cosB=$\frac { 12 }{ 13 } ,\frac { 3\pi }{ 2 }$$\pi$, find cos(A+B)

10. Prove that $\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x }$

11. In a ΔABC if a=3, b=5 and c=7, find cosA and cosB.

12. 5 x 3 = 15
13. 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)

14. Find cos(x - y), given that cos x = $-\frac{4}{5}$ with $\pi<x<{{3\pi}\over{2}}$ and sin y = $-\frac{24}{25}$ with$\pi<y<{{3\pi}\over{2}}$.

15. if a cos $\theta$ -b sin $\theta$ = C Show that a sin $\theta$ +b cos $\theta$ = $\pm \sqrt { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } }$

16. Prove that cos $\left( {{3\pi}\over{4}}+\pi\right)-cos\left({{3\pi}\over{4}}-4\right)=-\sqrt{2}sin\ x.$

17. If $2cos\theta=x+\frac{1}{x}$ then prove that $2\theta=\frac{1}{2}(x^2+\frac{1}{x^2})$

18. 4 x 5 = 20
19. if sin $\theta$ + cos $\theta$ = m, show that cos6$\theta$ + sin6$\theta$  = $\frac { 4-3({ m }^{ 2 }-1)^{ 2 } }{ 4 }$ where m2 $\le$ 2

20. Prove that $sin\frac { \theta }{ 2 } sin\frac { 7\theta }{ 2 } +sin\frac { 3\theta }{ 2 } sin\frac { 11\theta }{ 2 } =sin2\theta sin5\theta$

21. If the sides of a $\triangle$ABC are a = 4, b = 6, and c = 8, show that $4\cos { B } +3\cos { C } =2$

22. Show that $\sin ^{ -1 }{ \left( \frac { 12 }{ 13 } \right) } +\cos ^{ -1 }{ \left( \frac { 4 }{ 5 } \right) } +\tan ^{ -1 }{ \left( \frac { 63 }{ 16 } \right) } =\pi$