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Simplify : tan^-1((cosx - sinx)/(cosx + sinx)), 0 < x < π

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Simplify : tan-1((cosx - sinx)/(cosx + sinx)), 0 < x < π

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(inside the bracket divide numerator and denominator by cos x)

= tan-1((1 - tanx)/(1 + tanx)) = tan-1(tan(π/4 - x)) (∵ tan(π/4 - x) = (1 - tanx)/(1 + tanx))

= π/4 - x

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