MHT CET · Maths · Differentiation
\(y=\log \tan x / 2+\sin ^{-1}(\cos x)\), then \(d y / d x\) is
- A \(\operatorname{cosec} x-1\)
- B \(\operatorname{cosec} x\)
- C \(\operatorname{cosec} x+1\)
- D \(x\)
Answer & Solution
Correct Answer
(A) \(\operatorname{cosec} x-1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \frac{d y}{d x} &=\frac{1}{\tan x / 2} \sec ^{2} \frac{x}{2} \cdot \frac{1}{2}+\frac{1}{\sqrt{1-\cos ^{2} x}}(-\sin x) \\ &=\frac{1}{2 \sin \frac{x}{2} \cdot \cos \frac{x}{2}}-1=\operatorname{cosec} x-1 \end{aligned}\)
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