[ ( ^ -1 3 4 ) ]^2= - Vidyadip

MCQ

$\left[\sin \left(\tan ^{-1} \frac{3}{4}\right)\right]^2=$

A
$\frac{3}{5}$
B
$\frac{5}{3}$
✓
$\frac{9}{25}$
D
$\frac{25}{9}$

✓

Answer

Correct option: C.

$\frac{9}{25}$

(C) $\left[\sin \left(\tan ^{-1} \frac{3}{4}\right)\right]^2$
$=\left[\sin \left\{\sin ^{-1}\left(\frac{\frac{3}{4}}{\sqrt{1+\left(\frac{3}{4}\right)^2}}\right)\right]\right]^2$ $\ldots\left[\because \tan ^{-1} x=\sin ^{-1}\left(\frac{x}{\sqrt{1+x^2}}\right)\right]$
$=\left[\sin \left(\sin ^{-1} \frac{3}{5}\right)\right]^2=\left(\frac{3}{5}\right)^2=\frac{9}{25}$

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