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  • The value of sin inverse into bracket cos into bracket 33 pi divided 5 is A. 3pi divided 5 B. -7pi divided 5 C. pi divided 10 D. -pi divided 10

The value of \sin^{-1}\left [ cos\left ( \frac{33\pi}{5} \right ) \right ] is

A. \frac{3\pi}{5}

B. \frac{-7\pi}{5}

C. \frac{\pi}{10}

D. \frac{-\pi}{10}

Answers (1)

Answer :(D)

We have

\sin^{-1}\left [ \cos\left ( \frac{33\pi}{5} \right ) \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 ] \left [ Since , \cos\left ( 2n \pi+\theta \right ) = \cos\theta \right ]

=\sin^{-1}\left [ \cos \left ( \frac{\pi}{2}+\frac{\pi}{10} \right ) \right ]

=\sin^{-1}\left [ \sin \left (- \frac{\pi}{10} \right ) \right ]\left [ Since, \sin^{-1}\left ( x \right )=-\sin^{-1}x \right ]

=- \frac{\pi}{10} \left [ Since, \sin^{-1}\left ( \sin x \right )=-x, x\epsilon \left ( -\frac{\pi}{2} ,\frac{\pi}{2} \right ) \right ]

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