The value of sin−1⁡cos⁡33π5, is

The value of $\sin^{- 1} \{\cos (\frac{33 π}{5})\},$ is

A
$\frac{3 π}{5}$
B
$\frac{7 π}{5}$
C
$\frac{π}{10}$
D
$\frac{- π}{10}$

Solution:

We have,

$\begin{array}{l} \sin^{- 1} \{\cos (6 π + \frac{3 π}{5})\} \\ = \sin^{- 1} (\cos \frac{3 π}{5}) \end{array}$

$\begin{array}{l} = \sin^{- 1} \{\sin (\frac{π}{2} - \frac{3 π}{5})\} \\ = \sin^{- 1} \{\sin (\frac{- π}{10})\} = - \frac{π}{10} \end{array}$

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