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

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