AP EAMCET · Maths · Indefinite Integration
\(\int(1-\cos x) \operatorname{cosec}^2 x d x\) is equal to
- A \(\tan \left(\frac{x}{2}\right)+c\)
- B \(-\tan \left(\frac{x}{2}\right)+c\)
- C \(2 \tan \left(\frac{x}{2}\right)+c\)
- D \(-2 \tan \left(\frac{x}{2}\right)+c\)
Answer & Solution
Correct Answer
(A) \(\tan \left(\frac{x}{2}\right)+c\)
Step-by-step Solution
Detailed explanation
Let \(I=\int(1-\cos x) \operatorname{cosec}^2 x d x\) \(I=\int \operatorname{cosec}^2 x d x-\int \cos x \cdot \operatorname{cosec}^2 x d x\) \(\begin{aligned} & =-\cot x-\int \cos x \cdot \operatorname{cosec} x d x \\ & =-\cot x+\operatorname{cosec} x+C\end{aligned}\)…
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