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Question: Answered & Verified by Expert
$2 \sin ^{-1} \frac{3}{5}+\cos ^{-1} \frac{24}{25}=$
MathematicsInverse Trigonometric FunctionsJEE Main
Options:
  • A $\frac{\pi}{2}$
  • B $\frac{2 \pi}{3}$
  • C $\frac{5 \pi}{3}$
  • D None of these
Solution:
1674 Upvotes Verified Answer
The correct answer is: $\frac{\pi}{2}$
$\begin{aligned} & 2 \sin ^{-1} \frac{3}{5}+\cos ^{-1} \frac{24}{25}=\sin ^{-1} 2 \times \frac{3}{5} \sqrt{1-\frac{9}{25}}+\cos ^{-1} \frac{24}{25} \\ & \quad=\sin ^{-1} \frac{24}{25}+\cos ^{-1} \frac{24}{25}=\frac{\pi}{2}\end{aligned}$

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