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Find the value of the following:\sin\left[ {\frac{\pi }{3} - {{\sin }^{ - 1}}\left( { - \frac{1}{2}} \right)} \right]

Option: 1 43832

Option: 2 1

Option: 3 0

Option: 4 none of these

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As we learnt

 

Important Results of Inverse Trigonometric Functions -

 

\sin ^{-1}\left ( -x \right )= -\sin ^{-1}x

-

 

\sin\left[ {\pi /3 - {{\sin }^{ - 1}}\left( { - 1/2} \right)} \right]

= \sin\left[ {\frac{\pi }{3} - \left\{ { - {{\sin }^{ - 1}}\left( {\frac{1}{2}} \right)} \right\}} \right]    [\because sin^{-1}(-x) = -sin^{-1}x]

= \sin\left[ {\pi /3 + \pi /6} \right]$ = \sin\frac{\pi }{2} = 1.

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Pankaj Sanodiya

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