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\(\cos x\cos \left( \frac { \pi }{ 3 } -x \right) cos\left( \frac { \pi }{ 3 } +x \right)=\frac14 cos3x\)

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