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Prove that cot^(-1)((sqrt(1+x)-sqrt(1-x)...

Prove that `cot^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)+(1)/(2)cos^(-1)x`

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underset(xrarr0)lim (sqrt(1+x^2)-sqrt(1+x))/(sqrt(1+x^2)+sqrt(1+x))