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Question
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Solution
LHS = `2tan^-1(1/2)+tan^-1(1/7)`
`=tan^-1{(2xx1/2)/(1-(1/2)^2)}+tan^-1 1/7` `[because2tan^-1x=tan^-1{(2x)/(1-x^2)}]`
`=tan^-1{1/(3/4)}+tan^-1 1/7`
`=tan^-1 4/3+tan^-1 1/7`
`=tan^-1((4/3+1/7)/(1-4/3xx1/7))` `[because tan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))]`
`=tan^-1((31/21)/(17/21))`
`=tan^-1 31/17=`RHS
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