#### Trigonometry - Important Question Paper

11th Standard

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Maths

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

Part A

10 x 1 = 10
1. cos10+cos20+cos30+: : :+cos1790=

(a)

0

(b)

1

(c)

-1

(d)

89

2. Let fk(x)=$\frac { 1 }{ k }$[sinkx+coskx] where x$\in$R and k≥1. Then f4(x)-f6(x)=

(a)

$\frac { 1 }{ 4 }$

(b)

$\frac { 1 }{ 12 }$

(c)

$\frac { 1 }{ 6 }$

(d)

$\frac { 1 }{ 3 }$

3. Which of the following is not true?

(a)

sinፀ=-$\frac { 3 }{ 4 }$​​​​​​​

(b)

cosፀ=-1

(c)

tanፀ=25

(d)

secፀ=$\frac { 1 }{ 4 }$

4. If tan α and tan β are the roots of tan x2+atanx+b=0; then $\frac { sin(\alpha +\beta ) }{ sin\alpha sin\beta }$ is equal to

(a)

$\frac { b }{ a }$

(b)

$\frac { a }{ b }$

(c)

$\frac { a }{ b }$

(d)

$\frac { b}{ a }$

5. In a triangle ABC, sin2A+sin2B+sin2C=2, then the triangle is

(a)

equilateral triangle

(b)

isosceles triangle

(c)

right triangle

(d)

scalene triangle

6. A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

(a)

10$\pi$ seconds

(b)

20$\pi$ seconds

(c)

5$\pi$ seconds

(d)

15$\pi$ seconds

7. If A + B = 45° then tan A - tan B + tan A tan B is

(a)

2

(b)

0

(c)

1

(d)

-1

8. The value of sin${\pi\over 48}cos {\pi \over 48} cos {\pi \over 24}cos {\pi \over 12}cos{\pi \over 6}cos {\pi \over 3}$ is

(a)

$\sqrt{3}\over32$

(b)

$\sqrt{3}\over64$

(c)

${3}\over32$

(d)

${3}\over64$

9. In a $\triangle$ ABC, C = 90° then the value of sin A + sin B-2$\sqrt{2} cos{A\over2}cos {B\over 2}is$

(a)

-1

(b)

1

(c)

0

(d)

${1\over 2}$

10. The general solution of cosec$\theta$ = -2 is

(a)

$2n\pi +(-1)^n({\pi\over 6})$

(b)

$n\pi +(-1)^n({-\pi\over 6})$

(c)

$2n\pi \pm({\pi\over 6})$

(d)

$-{\pi\over 6}+n\pi$

11. Part B

6 x 2 = 12
12. Find the values of cos x and tan x if $\sin x=-\frac{3}{5}$ and $\pi < x < \frac{3\pi}{2}$

13. Evaluate tan 4800

14. cot B - cot A = b, tan A - tan B = a, find cot (A - B).

15. Simplify: cos A + cos (120° + A) + cos (120° - A)

16. Find the values of sin(480°).

17. Find the values of sin(-1110°).

18. Part C

6 x 3 = 18
19. If any $\triangle ABC$ prove that $\frac { \sin { B } }{ \sin { C } } =\frac { c-a\cos { B } }{ b-a\cos { C } }$.

20. Two slopes leave a port at the same time one goes 24 km/hr in the direction N 45o E and other travels 32 km/hr in the direction S 75o E. Find the distance between the ships at the end of 3 hours.

21. Solve: sin 2x + cos x = 0

22. Prove that cos-1 x = $2\sin ^{ -1 }{ \sqrt { \frac { 1-x }{ 2 } } } =2\cos ^{ -1 }{ \sqrt { \frac { 1+x }{ 2 } } }$

23. Prove that $\tan ^{ -1 }{ \left( \frac { x }{ \sqrt { { { a }^{ 2 }-{ x }^{ 2 } } } } \right) } =\sin ^{ -1 }{ \left( \frac { x }{ a } \right) }$

24. Prove that $cos\left( \frac { \pi }{ 4 } -A \right) cos\left( \frac { \pi }{ 4 } -B \right) -sin\left( \frac { \pi }{ 4 } -A \right) sin\left( \frac { \pi }{ 4 } -B \right)$

25. Part D

2 x 5 = 10
26. If 3 tanA tan B=1, prove that 2 cos(A+B)=cos(A-B)

27. Prove that$\cos x\cos \left( \frac { \pi }{ 3 } -x \right) cos\left( \frac { \pi }{ 3 } +x \right)=\frac14 cos3x$