MHT CET · Maths · Inverse Trigonometric Functions
The principal value of \(\sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)\) is
- A \(\frac{\pi}{4}\)
- B \(\frac{3 \pi}{4}\)
- C \(\frac{-\pi}{4}\)
- D \(\frac{5 \pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \sin ^{-1}\left(\sin \frac{3 \pi}{4}\right) & =\sin ^{-1}\left[\sin \left(\pi-\frac{\pi}{4}\right)\right] \\ & =\sin ^{-1}\left(\sin \frac{\pi}{4}\right) \\ & =\frac{\pi}{4}\end{aligned}\)
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