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Prove that i) tan^(-1)(1+x)/(1-x)=pi/4...

Prove that
i) `tan^(-1)(1+x)/(1-x)=pi/4 + tan^(-1)x,x lt 1`
ii) `tan^(-1)x+cot^(-1)(x+1)=tan^(-1)(x^(2)+x+1)`

Text Solution

Verified by Experts

i) Put `x=tantheta`, ii) LHS `=tan^(-1)x+1/(tan^(-1)(x+1))`
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