Prove that 1+cos4x/cosx-tanx = 1/2 sin 4x
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I= ∫1+ cos4x*sinx* cosx/(cos2x-sin2x) dx
= ∫1+ (2cos22x-1)*sin2x/2cos2x dx
let cos2x = t
I= ∫1+ (2t2-1)/(-4t) dt
=∫(1-t/2+1/4t) dt
=t - t2/4 + 1/4 ln t + c where cos2x=t
I= ∫1+ cos4x*sinx* cosx/(cos2x-sin2x) dx
= ∫1+ (2cos22x-1)*sin2x/2cos2x dx
let cos2x = t
I= ∫1+ (2t2-1)/(-4t) dt
=∫(1-t/2+1/4t) dt
=t - t2/4 + 1/4 ln t + c where cos2x=t
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