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Prove that: tan^(-1)(2/11)+tan^(-1)(7/24...

Prove that: `tan^(-1)(2/11)+tan^(-1)(7/24)=tan^(-1)(1/2)`

Text Solution

Verified by Experts

We know, `tan^-1x+tan-^-1y = tan^-1((x+y)/(1-xy))`
So, `L.H.S. = tan^-1(2/11)+tan^-1(7/24)`
`=tan^-1((2/11+7/24)/(1-2/11**7/24))`
`=tan^-1(125/250)`
`=tan^-1(1/2)=R.H.S.`
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