[ 2 ^ - 1 1 5 + ^ - 1 1 5 ] = - Vidyadip

MCQ

$\cos \left[ {2{{\cos }^{ - 1}}\frac{1}{5} + {{\sin }^{ - 1}}\frac{1}{5}} \right] = $

A
$\frac{{2\sqrt 6 }}{5}$
✓
$ - \frac{{2\sqrt 6 }}{5}$
C
$\frac{1}{5}$
D
$ - \frac{1}{5}$

✓

Answer

Correct option: B.

$ - \frac{{2\sqrt 6 }}{5}$

b
(b) $\cos \,\left( {{{\cos }^{ - 1}}\frac{1}{5} + {{\sin }^{ - 1}}\frac{1}{5} + {{\cos }^{ - 1}}\frac{1}{5}} \right) = \cos \,\left( {\frac{\pi }{2} + {{\cos }^{ - 1}}\frac{1}{5}} \right)$

$ = - \sin \,\left( {{{\cos }^{ - 1}}\frac{1}{5}} \right) = - \sin \,\left( {{{\sin }^{ - 1}}\sqrt {\frac{{24}}{{25}}} } \right) = - \frac{{2\sqrt 6 }}{5}$.

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