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TS EAMCET · Maths · Indefinite Integration

If \(\int \frac{\sin x}{\cos x(1+\cos x)} d x=f(x)+c\), then \(f(x)\) is equal to

  1. A \(\log \left|\frac{1+\cos x}{\cos x}\right|\)
  2. B \(\log \left|\frac{\cos x}{1+\cos x}\right|\)
  3. C \(\log \left|\frac{\sin x}{1+\sin x}\right|\)
  4. D \(\log \left|\frac{1+\sin x}{\sin x}\right|\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\log \left|\frac{1+\cos x}{\cos x}\right|\)

Step-by-step Solution

Detailed explanation

\(\text { Let } I=\int \frac{\sin x}{\cos x(1+\cos x)} d x\) Put \(\cos x=t \Rightarrow-\sin x d x=d t\)…