, [ ^ - 1 ( 3 5 ) + ^ - 1 2 ] = - Vidyadip

MCQ

$\sin \,\left[ {{{\cos }^{ - 1}}\left( {\frac{3}{5}} \right) + {{\tan }^{ - 1}}2} \right]$ =

✓
$\frac{2}{{\sqrt 5 }}$
B
$\frac{-2}{{\sqrt 5 }}$
C
$\frac{3}{{\sqrt 5 }}$
D
$\frac{-3}{{\sqrt 5 }}$

✓

Answer

Correct option: A.

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

a
$\sin \left[\sin ^{-1}\left(\frac{4}{5}\right)+\sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right]$

$=\sin \left[\sin ^{-1}\left(\frac{4}{5} \sqrt{1-\frac{4}{5}}+\frac{2}{\sqrt{5}}\right)\right]$

$=\sin \left[\sin ^{-1}\left(\frac{10}{5 \sqrt{5}}\right)\right]$

$=\frac{2}{\sqrt{5}}$

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