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Inverse Trigonometric Functions Model Question Paper

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. If sin-1 x+sin-1 y=\(\frac{2\pi}{3};\)then cos-1x+cos-1 y is equal to

    (a)

    \(\frac{2\pi}{3}\)

    (b)

    \(\frac{\pi}{3}\)

    (c)

    \(\frac{\pi}{6}\)

    (d)

    \(\pi\)

  2. If cot−1x=\(\frac{2\pi}{5}\) for some x\(\in\)R, the value of tan-1 x is

    (a)

    \(\frac{-\pi}{10}\)

    (b)

    \(\frac{\pi}{5}\)

    (c)

    \(\frac{\pi}{10}\)

    (d)

    \(-\frac{\pi}{5}\)

  3. If the function f(x)sin-1(x2-3), then x belongs to

    (a)

    [-1,1]

    (b)

    [\(\sqrt2\),2]

    (c)

    \(\\ \\ \\ \left[ -2,-\sqrt { 2 } \right] \cup \left[ \sqrt { 2 } ,2 \right] \)

    (d)

    \(\left[ -2,-\sqrt { 2 } \right] \cap \left[ \sqrt { 2 } ,2 \right] \)

  4. The value of \({ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right) \) is 

    (a)

    \(\cfrac { \pi }{ 2 } \)

    (b)

    \(\cfrac { 5\pi }{ 3 } \)

    (c)

    \(\cfrac { 10\pi }{ 3 } \)

    (d)

    0

  5. If \({ tan }^{ -1 }\left( \cfrac { x+1 }{ x-1 } \right) +{ tan }^{ -1 }\left( \cfrac { x-1 }{ x } \right) ={ tan }^{ -1 }\left( -7 \right) \) then x Is

    (a)

    0

    (b)

    -2

    (c)

    1

    (d)

    2

  6. 5 x 2 = 10
  7. For what value of x does sinx=sin−1x?

  8. Find the value of sin-1\(\left( sin\frac { 5\pi }{ 9 } cos\frac { \pi }{ 9 } +cos\frac { 5\pi }{ 9 } sin\frac { \pi }{ 9 } \right) \).

  9. Find all values of x such that
    6\(\pi\le x \le 6\pi\) and cos x -0 

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

  11. Ecalute \(sin\left( { cos }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) \right) \)
     

  12. 5 x 3 = 15
  13. For what value of x , the inequality\(\cfrac { \pi }{ 2 } <{ cos }^{ -1 }(3x-1)<\pi \)

  14. Find the value of
     \(cos\left( { cos }^{ -1 }\left( \frac { 4 }{ 5 } \right) +{ sin }^{ -1 }\left( \frac { 4 }{ 5 } \right) \right) \)

  15. Prove that tan(sin-1x)=\(\frac{x}{\sqrt1-x^2},-1<x<1.\)

  16. Solve \({ tan }^{ -1 }\left( \cfrac { 2x }{ 1-{ x }^{ 2 } } \right) +{ cot }^{ -1 }\left( \cfrac { 1-{ x }^{ 2 } }{ 2x } \right) =\cfrac { \pi }{ 3 } ,x>0\)

  17. If \(sin\left( { sin }^{ -1 }\cfrac { 1 }{ 5 } +{ cos }^{ -1 }x \right) =1\) then find the value ofx.

  18. 4 x 5 = 20
  19. Find the principal value of cos−1\(\left( \frac { \sqrt { 3 } }{ 3 } \right) \)

  20. Solve \(tan^{ -1 }\left( \frac { x-1 }{ x-2 } \right) +tan^{ -1 }\left( \frac { x+1 }{ x+2 } \right) =\frac { \pi }{ 4 } \)

  21. Write thefunction\(f(x)={ tan }^{ -1 }\sqrt { \cfrac { a-x }{ a+x } } -a<x<a\) in the simplest form
     

  22. Provethat \({ tan }^{ -1 }\left( \cfrac { 1-x }{ 1+x } \right) -{ tan }^{ -1 }\left( \cfrac { 1-y }{ 1+y } \right) ={ sin }^{ -1 }\left( \cfrac { y-x }{ \sqrt { 1+{ x }^{ 2 } } .\sqrt { 1+{ y }^{ 2 } } } \right) \\ \)

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