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Question: If \(\sin \left( \sin ^ { - 1 } \frac { 1 } { 5 } + \cos ^ { - 1 } x \right) = 1\),then x is equal t...

If sin⁡(sin⁡−115+cos⁡−1x)=1\sin \left( \sin ^ { - 1 } \frac { 1 } { 5 } + \cos ^ { - 1 } x \right) = 1,then x is equal to.

A

1

B

0

C

45\frac { 4 } { 5 }

D

15\frac { 1 } { 5 }

Answer

15\frac { 1 } { 5 }

Explanation

Solution

sin⁡−115+cos⁡−1x=π2\sin ^ { - 1 } \frac { 1 } { 5 } + \cos ^ { - 1 } x = \frac { \pi } { 2 }

∴sin⁡−115=π2−cos⁡−1x=sin⁡−1x\therefore \sin ^ { - 1 } \frac { 1 } { 5 } = \frac { \pi } { 2 } - \cos ^ { - 1 } x = \sin ^ { - 1 } x

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