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Question
Find :
`∫ sin(x-a)/sin(x+a)dx`
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Solution
`∫ sin(x-a)/sin(x+a)dx`
`I = ∫ sin(x-a)/sin(x+a)dx`
= `∫sin(x-a+a-a)/sin(x+a)dx`
= `∫sin(x+a-2a)/sin(x+a)dx`
= `∫(sin(x+a) cos2a - sin 2acos(x+a))/sin(x+a)dx`
= `∫ cos 2a dx - ∫ sin 2acot(x+a)dx`
`I = x cos 2a - sin 2a log |sin(x+a)|+C`
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