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∫ \(\frac{1+tan\,x\,.\,tan(x+\theta)}{[tan(x+\theta)-tan\,x]}\) (tan(x+θ) - tan x)dx
= ∫ \(\frac1{tan\,\theta}\) [tan(x+θ) - tan x] . dx
= \(\frac1{tan\,\theta}\) ∫ tan(x+θ)dx - ∫ tan x . dx
= \(\frac1{tan\,\theta}\) [-log cos(x+θ)1] + [log |cos x|] + c
= \(\frac1{tan\,\theta}\) log |\(\frac{cos\,x}{cos(x+\theta)}\)| + c
= cot θ log |\(\frac{cos\,x}{cos(x+\theta)}\)| + c.
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