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Prove that tan^-1(1/7)+tan^-1(1/13)=tan^...

Prove that `tan^-1(1/7)+tan^-1(1/13)=tan^-1(2/9)`

Text Solution

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L.H.S. `=tan^(-1)+tan^(-1)(1/13)`
`:' 1/7xx1/13lt1`
`:." Using "tan^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy)),xy lt 1`
We get `tan^(-1)(1/7)+tan^(-1)(1/13)`
`=tan^(-1)((1/7+1/13)/(1-1/7xx1/13))`
`tan^(-1)((13+7)/(91-1))`
`=tan^(-1)(20/90)`
`tan^(-1)(2/9)=R.H.S.`
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