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Prove that: 2tan^(-1)1/2+tan^(-1)1/7=tan...

Prove that: `2tan^(-1)1/2+tan^(-1)1/7=tan^(-1)(31)/(17)`

Text Solution

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`LHS=2tan^(-1)(1)/(2)+tan^(-1)(1)/(7)`
`=tan^(-1)((2xx(1)/(2))/(1-(1)/(4)))+tan^(-1)""(1)/(7)`
`=tan^(-1)""(4)/(3)+tan^(-1)"'(1)/(7)`
`tan^(-1)""((4)/(3)+(1)/(7))/(1-(4)/(3)xx(1)/(7))=tan^(-1)((28+3)/(21))/((21-4)/(21))`
`=tan^(-1)""(31)/(17)=` RHS Hence Proved.
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