[3 ^ -1 (1 5 ) ]= - Vidyadip

MCQ

$\sin \left[3 \sin ^{-1}\left(\frac{1}{5}\right)\right]=$

✓
$\frac{71}{125}$
B
$\frac{74}{125}$
C
$\frac{3}{5}$
D
$\frac{1}{2}$

✓

Answer

Correct option: A.

$\frac{71}{125}$

(A) $\sin \left[3 \sin ^{-1}\left(\frac{1}{5}\right)\right]=\sin \left[\sin ^{-1}\left\{3\left(\frac{1}{5}\right)-4\left(\frac{1}{5}\right)^3\right\}\right]$
$=\sin \left[\sin ^{-1}\left\{\frac{3}{5}-\frac{4}{125}\right\}\right]=\sin \left[\sin ^{-1}\left(\frac{75-4}{125}\right)\right]$
$=\sin \left[\sin ^{-1} \frac{71}{125}\right]=\frac{71}{125}$

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