AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), then \(\cos ^{-1}(\sin \theta)\) is equal to
- A \(\frac{\pi}{2}-\theta\)
- B \(\theta-\frac{\pi}{2}\)
- C \(\frac{\pi}{2}+\theta\)
- D \(\pi+\frac{\theta}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}-\theta\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right], \cos ^{-1}(\sin \theta)=? \\ & \Rightarrow \quad \cos ^{-1}\left[\cos \left(\frac{\pi}{2}-\theta\right)\right]=\left(\frac{\pi}{2}-\theta\right) \end{aligned}\)
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