Question

(b) If \( \sin^{-1} \left( \frac{1}{2} \right) = \tan^{-1} x \), then find the value of \( x \).

Hint:

Use trigonometric identities like \(\tan^{-1} x = \tan(\theta)\) to simplify and compare values.

Answer 1

Usingthetrigonometricidentity: \[ \sin^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}\quad\text{and}\quad\tan^{-1}x=\frac{\pi}{6}. \] Therefore,\(x=\tan\left(\frac{\pi}{6}\right)=\frac{1}{\sqrt{3}}\).