cos^(-1)((sin x+cos x)/(sqrt(2))),(-pi)/(4)

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Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (pi)/(4)

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arctan^(-1)((cos x)/(1-sin x))-cos^(-1)(sqrt((1+cos x)/(1-cos x)))=(pi)/(4),x in(0,(pi)/(2))