Question

The value of \(sin^{-1} [cos(sin^{-1}\frac {\sqrt{3}}{2})]\) is:

• A. \(\frac {\Pi}{6}\)
• B. \(\frac {\Pi}{3}\)
• C. \(\frac {\Pi}{2}\)
• D. \(\frac {\Pi}{4}\)

Answer 1

The Correct Option is A

To find the value of \(sin^{-1} [cos(sin^{-1}\frac {\sqrt{3}}{2})]\), follow these steps:

1. Start with the expression \(sin^{-1}\frac {\sqrt{3}}{2}\). We need to determine the angle \(\theta\) such that \(sin(\theta) = \frac{\sqrt{3}}{2}\).

2. The angle \(\theta\) for which \(sin(\theta) = \frac{\sqrt{3}}{2}\) is \(\theta = \frac{\pi}{3}\).

3. Now, substitute \(\theta\) into the cosine function: \(cos(\frac{\pi}{3})\).

4. Calculate: \(cos(\frac{\pi}{3}) = \frac{1}{2}\).

5. We need to find \(sin^{-1}(\frac{1}{2})\). The angle \(\phi\) such that \(sin(\phi) = \frac{1}{2}\) is \(\phi = \frac{\pi}{6}\).

6. Therefore, the value of \(sin^{-1} [cos(sin^{-1}\frac {\sqrt{3}}{2})]\) is \(\frac {\pi}{6}\).