MHT CET · Maths · Inverse Trigonometric Functions
The principal value of \(\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)\) is
- A \(-\left(\frac{2 \pi}{3}\right)\)
- B \(\left(\frac{5 \pi}{3}\right)\)
- C \(\left(\frac{\pi}{3}\right)\)
- D \(\left(\frac{2 \pi}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{\pi}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)=\sin ^{-1}\left(\sin \left(\pi-\frac{2 \pi}{3}\right)\right)=\sin ^{-1}\) \(\left(\sin \left(\frac{\pi}{3}\right)\right)\) \(=\frac{\pi}{3}\)
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