We have to find the integral of y = (cos x)^2 - (sin x)^2.
We know that cos 2x = (cos x)^2 - (sin x)^2
=> y = cos 2x
Int[ cos 2x dx]
let 2x = y, dy/2 = dx
=> Int[(1/2)cos y dy]
=> (1/2) sin y + C
substitute y = 2x
=> (1/2)*sin 2x + C
The required integral is (1/2)*sin 2x + C
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