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

Prove that `tan^(-1) x + cot^(-1) (x+1) = tan ^(-1) (x^(2) + x+1)`.

Text Solution

Verified by Experts

L.H.S =` tan^(-1).(1)/(4) + tan^(-1) .(2)/(9)`
`= tan^(-1).((1)/(4)+(2)/(9))/(1-(1)/(4) xx(2)/(9))`
`= tan^(-1).(x+(1)/(x+1))/(1-x.(1)/(x+1))= tan ^(-1).(x(x-1)+1)/((x+ 1)-x)`
`tan^(-1) (x^(2) + x+1)`
= R.H.S
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