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Question: Answered & Verified by Expert
If $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$, then the value of $x$ is
MathematicsInverse Trigonometric FunctionsMHT CETMHT CET 2022 (05 Aug Shift 1)
Options:
  • A $\frac{\pi}{2}+\frac{1}{5}$
  • B $\frac{\pi}{2}-\frac{1}{5}$
  • C $-\frac{1}{5}$
  • D $\frac{1}{5}$
Solution:
2274 Upvotes Verified Answer
The correct answer is: $\frac{1}{5}$
$\begin{aligned} & \sin \sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1=\sin \frac{\pi}{2} \\ & \Rightarrow \sin ^{-1} \frac{1}{5}+\cos ^{-1} x=\frac{\pi}{2} \\ & \Rightarrow \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} \frac{1}{5} \\ & \Rightarrow \cos ^{-1} x=\cos ^{-1} \frac{1}{5} \\ & \Rightarrow x=\frac{1}{5}\end{aligned}$

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