If ( ^ - 1 1 5 + ^ - 1 x ) = 1, then x is equal to - Vidyadip

MCQ

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

A
$1$
B
$0$
C
$\frac{4}{5}$
✓
$\frac{1}{5}$

✓

Answer

Correct option: D.

$\frac{1}{5}$

d
(d) ${\sin ^{ - 1}}\frac{1}{5} + {\cos ^{ - 1}}x = \frac{\pi }{2}$

$\therefore \,\,{\sin ^{ - 1}}\frac{1}{5} = \frac{\pi }{2} - {\cos ^{ - 1}}x = {\sin ^{ - 1}}x$

$\therefore \,\,\,x = \frac{1}{5}$.

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