KCET · Maths · Mathematical Reasoning
The value of \( \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)+\sin ^{-1}\left(\frac{1}{3}\right) \) is equal to
- A \( \frac{\pi}{6} \)
- B \( \frac{\pi}{2} \)
- C \( \frac{\pi}{4} \)
- D \( 2 \frac{\pi}{3} \)
Answer & Solution
Correct Answer
(B) \( \frac{\pi}{2} \)
Step-by-step Solution
Detailed explanation
\( \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)+\sin ^{-1}\left(\frac{1}{3}\right) = \sin^{-1}\left(\frac{2\sqrt{2}}{3}\sqrt{1-\left(\frac{1}{3}\right)^2} + \frac{1}{3}\sqrt{1-\left(\frac{2\sqrt{2}}{3}\right)^2}\right) \) \( = \sin^{-1}\left(\frac{2\sqrt{2}}{3}\sqrt{1-\frac{1}{9}} + \frac{1}{3}\sqrt{1-\frac{8}{9}}\right) \)
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