Inverse Trigonometric Functions Two Marks Questions

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. State the reason for cos-1\([cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.\)

  2. Is cos-1(-x)=\(\pi\)-cos−1(x) true? Justify your answer.

  3. Find the principal value of cos-1\((\frac{1}{2})\).

  4. Find the value of sec−1\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

  5. If cot-1\(\frac{1}{7}=\theta\), find the value of cos\(\theta\).
     

  6. Find the value of
     \({ tan }^{ -1 }\left( \sqrt { 3 } \right) -{ sec }^{ -1 }(-2)\)

  7. Find all the values of x such that
     -8\(\pi\)\(\le x\le\)-8\(\pi\) and sin x=-1

  8. Find the value of 
    tan (tan−1(-0.2021))

  9. Simplify
    sin-1[sin10]

  10. Find the value of 
    \(cos\left[ \frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 1 }{ 8 } \right) \right] \)
     

  11. If \({ cot }^{ -1 }\left( \cfrac { 1 }{ 7 } \right) =\theta \) find the value of cos \(\theta \)

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

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

  14. Prove that \(2{ tan }^{ -1 }\left( \cfrac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \cfrac { 12 }{ 5 } \right) \)
     

  15. Evaluate \(sin\left( { cos }^{ -1 }\left( \cfrac { 1 }{ 2 } \right) \right) \)
     

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