Search any question & find its solution
Question:
Answered & Verified by Expert
If $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$, then the value of $x$ is
Options:
Solution:
2274 Upvotes
Verified Answer
The correct answer is:
$\frac{1}{5}$
$\begin{aligned} & \sin \sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1=\sin \frac{\pi}{2} \\ & \Rightarrow \sin ^{-1} \frac{1}{5}+\cos ^{-1} x=\frac{\pi}{2} \\ & \Rightarrow \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} \frac{1}{5} \\ & \Rightarrow \cos ^{-1} x=\cos ^{-1} \frac{1}{5} \\ & \Rightarrow x=\frac{1}{5}\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.