AP EAMCET · Maths · Differentiation
If \(y=\tan ^{-1} \sqrt{\frac{1-\cos x}{1+\cos x}}\), then the values of \(\frac{d y}{d x}\) and \(\frac{d^2 y}{d x^2}\) respectively are
- A 1,0
- B \(\frac{x}{2}, \frac{1}{2}\)
- C \(\frac{1}{2}, 0\)
- D \(\frac{-1}{2}, 0\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}, 0\)
Step-by-step Solution
Detailed explanation
We have \(y=\tan ^{-1} \sqrt{\frac{1-\cos x}{1+\cos x}}\) \(\Rightarrow \quad y=\tan ^{-1} \sqrt{\frac{2 \sin ^2 x / 2}{2 \cos ^2 x / 2}}=\tan ^{-1}(\tan x / 2)\) \(\Rightarrow \quad y=x / 2 \Rightarrow \frac{d y}{d x}=\frac{1}{2}\) \(\Rightarrow \quad \frac{d^2 y}{d x^2}=0\)
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