Question

If \(\int \cos x \log \left(\tan \frac{x}{2}\right) d x=\sin x \log \left(\tan \frac{x}{2}\right)+f(x)\) then \(f(x)\) is equal to, (assuming \(c\) is a arbitrary real constant)
(A) \(\mathrm{C}\)
(B) \(c-x\)
(C) \(\mathrm{c}+\mathrm{x}\)
(D) \(2 x+c\)

Answer 1

Ans : (B)
Hint \(:\) IBP \(\Rightarrow I=\sin x \log \left(\tan \frac{x}{2}\right)-x+c\)
\(\therefore f(x)=c-x\)

Answer 2

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