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
- A \(-\frac{\pi}{2}\)
- B \(\pi\)
- C 0
- D \(\frac{\pi}{4}\)
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…
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