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Question
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
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Solution
Let I = `int cosx/sin(x - a).dx`
= `int cos[(x - a) + a]/sin(x - a).dx`
= `int[cos(x - a)cos a - sin(x - a)sin a)/sin(x - a).dx`
= `int [(cos(x - a)cos a)/sin(x - a) - (sin(x - a)sina)/sin(x - a)].dx`
= `cos a int cot (x - a)dx - sin a int 1 dx`
= cos a log |sin(x – a)| – x sin a + c.
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