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प्रश्न
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
विकल्प
`(3pi)/5`
`-pi/10`
`pi/10`
`(7pi)/5`
उत्तर
(b) `-pi/10`
\[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right) = \sin^{- 1} \left\{ \cos\left( 6\pi + \frac{3\pi}{5} \right) \right\}\]
\[ = \sin^{- 1} \left\{ \cos\left( \frac{3\pi}{5} \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( \frac{\pi}{2} - \frac{3\pi}{5} \right) \right\}\]
\[ = \frac{\pi}{2} - \frac{3\pi}{5}\]
\[ = - \frac{\pi}{10}\]
\[\]
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