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# 2. Inverse Trigonometric Functions

# Inverse Trigonometric Functions Class 12 Maths

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**Summary:**

The ranges (principal value branches) of inverse trigonometric functions are given in the following table:

Functions | Range |

\sin^{-1}x | \left[ \frac{-\pi}{2}, \frac{\pi}{2} \right] |

\csc^{-1}x | \left[ \frac{-\pi}{2}, \frac{\pi}{2} \right] – {0} |

\tan^{-1}x | \left( \frac{-\pi}{2}, \frac{\pi}{2} \right) |

\cos^{-1}x | [0, \pi] |

\sec^{-1}x | [0, \pi] – { \frac{\pi}{2} } |

\cot^{-1}x | (0, \pi) |

\sin^{-1}x should not be confused with (\sin x)^{-1}. In fact (\sin x)^{-1} = \frac{1}{\sin x} and similarly for other trigonometric functions.

The value of an inverse trigonometric functions which lies in its principal value branch is called the principal value of that inverse trigonometric functions.

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