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AP EAMCET · Maths · Indefinite Integration

If \(\int \frac{1}{1-\cos x} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c\), then one of the values of \(\frac{\pi \alpha}{4}-\beta\) is

  1. A \(-\frac{\pi}{2}\)
  2. B \(\pi\)
  3. C 0
  4. D \(\frac{\pi}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\pi\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \int \frac{1}{1-\cos x} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c \\ & \Rightarrow \int \frac{1}{2 \sin ^2 \frac{x}{2}} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c \\ & \Rightarrow \frac{1}{2} \int \operatorname{cosec}^2 \frac{x}{2} d x=\tan…