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
- A \(\log \left|\frac{1+\cos x}{\cos x}\right|\)
- B \(\log \left|\frac{\cos x}{1+\cos x}\right|\)
- C \(\log \left|\frac{\sin x}{1+\sin x}\right|\)
- D \(\log \left|\frac{1+\sin x}{\sin x}\right|\)
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 \(\cos x=t \Rightarrow-\sin x d x=d t\)…
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