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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 : 40
    7 x 1 = 7
  1. If \(\\ \\ \\ { cot }^{ -1 }\left( \sqrt { sin\alpha } \right) +{ tan }^{ -1 }\left( \sqrt { sin\alpha } \right) =u\), then cos2u is equal to

    (a)

    tan2\(\alpha\)

    (b)

    0

    (c)

    -1

    (d)

    tan2\(\alpha\)

  2. If |x|\(\le\)1, then 2tan-1 x-sin-1 \(\frac{2x}{1+x^2}\) is equal to

    (a)

    tan-1x

    (b)

    sin-1x

    (c)

    0

    (d)

    \(\pi\)

  3. If sin-1 \(\frac{x}{5}+ cosec^{-1}\frac{5}{4}=\frac{\pi}{2}\), then the value of x is

    (a)

    4

    (b)

    5

    (c)

    2

    (d)

    3

  4. sin(tan-1x), |x|<1 ia equal to

    (a)

    \(\frac{x}{\sqrt{1-x^2}}\)

    (b)

    \(\frac{1}{\sqrt{1-x^2}}\)

    (c)

    \(\frac{1}{\sqrt{1+x^2}}\)

    (d)

    \(\frac{x}{\sqrt{1+x^2}}\)

  5. The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    none

  6. \(sin\left\{ 2{ cos }^{ -1 }\left( \cfrac { -3 }{ 5 } \right) \right\} =\)

    (a)

    \(\cfrac { 6 }{ 15 } \)

    (b)

    \(\cfrac { 24 }{ 25 } \)

    (c)

    \(\cfrac { 4 }{ 5 } \)

    (d)

    \(\cfrac { -24 }{ 25 } \)

  7. The value of tan \(\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right) \) is ______

    (a)

    \(\cfrac { 19 }{ 8 } \)

    (b)

    \(\cfrac { 8 }{ 19 } \)

    (c)

    \(\cfrac { 19 }{ 12 } \)

    (d)

    \(\cfrac { 3 }{ 4 } \)

  8. 1 x 2 = 2
  9. (1) cot(cot-1(+600)) = -600
    (2) cot(cot-1(1782)) = 1782
    (3) \(cot\left( { cot }^{ -1 }\left( \cfrac { -17 }{ 9 } \right) \right) =\cfrac { -17 }{ 9 } \)
    (4) \(cot({ cot }^{ -1 }\left( \sqrt { 3 } \right) =\sqrt { 3 } \)

  10. 5 x 2 = 10
  11. Find the principal value of
     \({ Sin }^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

  12. Find all the values of x such that
    -10\(\pi\)\(\le x\le\)10\(\pi\) and sin x=0 

  13. Find the period and amplitude of
    y=4sin(−2x)

  14. Find the principal value of \({ cos }^{ -1 }\left( \cfrac { -1 }{ 2 } \right) \)

  15. If \({ sin }^{ -1 }\left( \cfrac { 1 }{ 2 } \right) ={ tan }^{ -1 }x\) then find the value of x,

  16. 2 x 3 = 6
  17. Find 
    i)  tan−1(\(-\sqrt3\))
    ii)  tan−1\((tan\frac{3\pi}{5})\)
    iii) tan(tan-1−(2019))

  18. Solve: cos(tan-1x) = \(sin\left( { cot }^{ -1 }\cfrac { 3 }{ 4 } \right) \) 

  19. 3 x 5 = 15
  20. Find (i) cos-1 \((-\frac{1}{\sqrt2})\)
    ii) cos-1\((cos(-\frac{\pi}{3}))\)
    iii) cos-1\((cos(-\frac{7\pi}{6}))\)

  21. Find the principal value of
    sec−1(−2).

  22. If \({ tan }^{ -1 }\left( \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right) =a\) than prove that x2=sin2a

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