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Basic Inverse Trigonometric Functions

If sin-1 x = ...

Question

If $s i n^{- 1} x = \frac{π}{5}$ for some $x ϵ (- 1, 1),$ then the value of $c o s^{- 1} x$ is
[IIT 1992]

A

$\frac{3 π}{10}$

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B

$\frac{5 π}{10}$

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C

$\frac{7 π}{10}$

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D

$\frac{9 π}{10}$

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Solution

The correct option is A
$\frac{3 π}{10}$

$s i n^{- 1} x + c o s^{- 1} x = \frac{π}{2} \Rightarrow c o s^{- 1} x = \frac{π}{2} - s i n^{- 1} x = \frac{π}{2} - \frac{π}{5} = \frac{3 π}{10.}$

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