Q55 / 170 · Manipal (MET) 2017 · Mathematics

If $4 \sin ^{-1} x+\cos ^{-1} x=\pi$, then $x$ is equal to

  • Correct answer
    A
    $\frac{1}{2}$
  • B
    2
  • C
    1
  • D
    $\frac{1}{3}$

Solution

Given, $4 \sin ^{-1} x+\cos ^{-1} x=\pi$ $\Rightarrow 4 \sin ^{-1} x+\frac{\pi}{2}-\sin ^{-1} x=\pi$ $\Rightarrow 3 \sin ^{-1} x=\frac{\pi}{2}$ $\Rightarrow x=\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}$

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

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