Question

The derivative of \(\tan^{-1}\!\sqrt{\dfrac{1-\cos x}{1+\cos x}}\) with respect to \(x\) is:

• A. \(1/4\)
• B. \(1/2\)
• C. 1
• D. \(-1/2\)

Hint:

Use half-angle identities to simplify.

Answer 1

The Correct Option is B

\[ \sqrt{\frac{1-\cos x}{1+\cos x}}=\tan\frac{x}{2} \Rightarrow y=\tan^{-1}\!\left(\tan\frac{x}{2}\right)=\frac{x}{2} \] \[ \frac{dy}{dx}=\frac12 \]