MCQ
${\sin ^{ - 1}}\left( {\cos \left( {{{\sin }^{ - 1}}x} \right)} \right) + {\cos ^{ - 1}}\left( {\sin \left( {{{\cos }^{ - 1}}x} \right)} \right) = ........$
- A$0$
- B$\frac{\pi }{4}$
- ✓$\frac{\pi }{2}$
- D$\frac{{3\pi }}{4}$
${\sin ^{ - 1}}\left( {\cos \left( {{{\sin }^{ - 1}}x} \right)} \right) + {\cos ^{ - 1}}\left( {\sin \left( {{{\cos }^{ - 1}}x} \right)} \right)$
$ = {\sin ^{ - 1}}\left( {\cos \left( {{{\cos }^{ - 1}}\sqrt {1 - {x^2}} } \right)} \right) + {\cos ^{ - 1}}\left( {\sin \left( {{{\sin }^{ - 1}}\sqrt {1 - {x^2}} } \right)} \right)$
$ = {\sin ^{ - 1}}\sqrt {1 - {x^2}} + {\cos ^{ - 1}}\sqrt {1 - {x^2}} $
$ = \frac{\pi }{2}$ $\because \left( {\sin x + \cos x = \frac{\pi }{2}} \right)$
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