Q42 / 120 · JEE Main 2007 · Mathematics

If $\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}$ then a value of $x$ is

  • A
    $1$
  • Correct answer
    B
    $3$
  • C
    $4$
  • D
    $5$

Solution

$\sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2}$ $\Rightarrow \sin ^{-1} \frac{x}{5}=\cos ^{-1} \frac{4}{5} \Rightarrow \sin ^{-1} \frac{x}{5}=\sin ^{-1} \frac{3}{5}$ $\therefore x=3$.

Hence, the correct answer is option: 'B'.

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