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 \(\sin { 2x } +\sin { 4x } +\sin { 6x } =0\)

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