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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