(3 ^ -1 (2 5 ) )= - Vidyadip

MCQ

$\sin \left(3 \sin ^{-1}\left(\frac{2}{5}\right)\right)=$

✓
$\frac{118}{125}$
B
$\frac{115}{127}$
C
$\frac{128}{135}$
D
$\frac{110}{118}$

✓

Answer

Correct option: A.

$\frac{118}{125}$

(A) $\sin \left(3 \sin ^{-1}\left(\frac{2}{5}\right)\right)=\sin 3 \theta$,
Where $\theta=\sin ^{-1}\left(\frac{2}{5}\right) \ldots\left[\theta=\sin ^{-1}\left(\frac{2}{5}\right), \sin \theta=\frac{2}{5}\right]$
$=3 \sin \theta-4 \sin ^3 \theta$
$=3\left(\frac{2}{5}\right)-4\left(\frac{2}{5}\right)^3 \ldots\left[\theta=\sin ^{-1}\left(\frac{2}{5}\right), \sin \theta=\frac{2}{5}\right]$
$=\frac{6}{5}-\frac{32}{125}=\frac{118}{125}$

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