AP EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{\sin (x-a) \cos (x-b)}=\)
- A \(\frac{1}{\sin (a-b)} \log \left|\frac{\sin (x-a)}{\cos (x-b)}\right|+C\)
- B \(\frac{1}{\cos (b-a)} \log \left|\frac{\sin (x-a)}{\cos (x-b)}\right|+C\)
- C \(\frac{1}{\cos (b-a)}[\log |\sin (x-a) \cos (x-b)|]+C\)
- D \(\frac{1}{\sin (a-b)}[\log |\sin (x-a) \cos (x-b)|]+C\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\cos (b-a)} \log \left|\frac{\sin (x-a)}{\cos (x-b)}\right|+C\)
Step-by-step Solution
Detailed explanation
\(\int \frac{d x}{\sin (x-a) \cos (x-b)}\) \(=\frac{1}{\cos (b-a)} \int \frac{\cos [(x-a)-(x-b)]}{\sin (x-a) \cos (x-b)}\) \(=\frac{1}{\cos (b-a)}\) \(\int\left[\frac{\cos (x-a) \cos (x-b)+\sin (x-a) \sin (x-b)}{\sin (x-a) \cos (x-b)}\right] d x\)…
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