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Question
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Solution
`int (cos 2x)/(sin^2x cos^2x) "d"x = int (cos^2x - sin^2alpha)/(sin^2x cos^2x) "d"x`
= `int ((cos^2x)/(sin^2x cos^2x) - (sin^2x)/(sin^2x cos^2x)) "d"x`
= `int (1/(sin^2x) - 1/(cos^2x)) "d"x`
= `int ("cosec"^2x - sec^2x) "d"x`
= `int "cosec"^2x "d"x - int sec^2x "d"x`
= `- cot x - tan x + "c"`
= `- [cosx/sinx + sinx/cosx] + "c"`
= `-[(cos^2x + sin^2x)/(sinx cosx)] + "c"`
= `- 2/(sin 2x) + "c"`
= – 2 cosec 2x + c
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