Evaluate: `intcos e c^2\ xcos^2 2x\ dx`

Explanation

Given,`∫ cosec^2x cos^2 2x dx`

= `∫cosec^2x(cos^2x-sin^2x)^2dx`

=`∫(cos^4x-2cos^2xsin^2x+sin^4x)/sin^2x dx`

=`int ((1-2sin^2x)(1-2sin^2x))/sin^2x-2cos^2x+sin^2x dx`

On multiplying` (1-sin^2x)(1-sin^2x)` equation reduces to,

=` ∫(cosec^2x-2+sin^2x-2cos^2x+ sin^2x)dx`

=` ∫(cosec^2x-2+2sin^2x-2cos^2x)dx `

=` ∫(-2(cos^2x-sin^2x)+cosec^2x-2)dx `

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