Mathematics - Inverse Trigonometric Functions

Question - 1

The value of sin \(\left[ \frac { \pi }{ 2 } -{ sin }^{ -1 }\left( -\frac { 1 }{ 2 } \right) \right] \) is

  • A \(\frac { \sqrt { 3 } }{ 4 } \)
  • B \(\frac { \sqrt { 3 } }{ 2 } \)
  • C \(-\frac { \sqrt { 3 } }{ 2 } \)
  • D \(-\sqrt { 3 } \)

Question - 2

Find the value of \(sin\left\{ \left( \frac { \pi }{ 2 } -{ sin }^{ -1 }\left( -\frac { \sqrt { 3 } }{ 2 } \right) \right) \right\} \)

  • A \(\frac { 1 }{ 3 } \)
  • B \(\frac { 1 }{ 2 } \)
  • C \(-\frac { 1 }{ 2 } \)
  • D \(\frac { 2 }{ 3 } \)

Question - 3

The value of \({ sin }^{ -1 }\left\{ cos\left( \frac { 43\pi }{ 5 } \right) \right\} \) is

  • A \(\frac { 3\pi }{ 5 } \)
  • B \(\frac { -7\pi }{ 5 } \)
  • C \(\frac { \pi }{ 10 } \)
  • D \(-\frac { \pi }{ 10 } \)

Question - 4

The angle \({ tan }^{ -1 }\left( tan\frac { 3\pi }{ 4 } \right) \) is

  • A \(\frac { \pi }{ 2 } \)
  • B \(-\frac { \pi }{ 3 } \)
  • C \(-\frac { \pi }{ 4 } \)
  • D \(\frac { \pi }{ 4 } \)

Question - 5

If \({ tan }^{ -1 }x=\frac { \pi }{ 10 } \) for some \(x\epsilon R\), then the value of cot-1 x is

  • A \(\frac { \pi }{ 5 } \)
  • B \(\frac { 2\pi }{ 5 } \)
  • C \(\frac { 3\pi }{ 5 } \)
  • D \(\frac { 4\pi }{ 5 } \)

Question - 6

The value of cos \(\left( { tan }^{ -1 }\frac { 3 }{ 4 } \right) \) is

  • A \(\frac { 3 }{ 2 } \)
  • B \(\frac { 1 }{ 2 } \)
  • C \(\frac { 4 }{ 5 } \)
  • D \(-\frac { 1 }{ 2 } \)

Question - 7

The range of \(f(x)=\left| { 3tan }^{ -1 }x-{ cos }^{ -1 }(0) \right| { -cos }^{ -1 }(-1)\) is

  • A \([-\pi ,\pi )\)
  • B \((-\pi ,\pi )\)
  • C \([-\pi ,\pi ]\)
  • D \(\left[ -\frac { \pi }{ 2 } ,\frac { \pi }{ 2 } \right) \)

Question - 8

The number of solutions of the equation cos ( cos-1 x) = cosec (cosec-1 x) is

  • A 2
  • B 3
  • C 4
  • D 1

Question - 9

\({ tan }^{ -1 }\sqrt { 3 } -{ cot }^{ -1 }(-\sqrt { 3 } )\) is equal to

  • A \(\pi \)
  • B \(-\frac { \pi }{ 2 } \)
  • C zero
  • D \(2\sqrt { 3 } \)

Question - 10

The value of cos (2cos-1 x + sin-1 x) at \(x=\frac { 1 }{ 5 } \) is

  • A 1
  • B 3
  • C 0
  • D \(-\frac { 2\sqrt { 6 } }{ 5 } \)
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