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tan^(-1)a+cot^(-1)(a+1)=tan^(-1)(a^2+a+1...

`tan^(-1)a+cot^(-1)(a+1)=tan^(-1)(a^2+a+1)`

Text Solution

Verified by Experts

`L.H.S. = tan^-1a+cot^-1(a+1)`
`= tan^-1a+tan^-1(1/(a+1))`
`= tan^-1((a+1/(a+1))/(1-a(1/(a+1))))`
`= tan^-1(((a^2+a+1)/(a+1))/((a+1-a)/(a+1)))`
`=tan^-1(a^2+a+1) = R.H.S.`
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