Prove that : `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot`

Explanation

Here, we will use,

`tan^-1x+tan^-1y = tan^-1((x+y)/(1-xy))`


`L.H.S. = tan^-1(1/2)+tan^-1(1/5)+tan^-1(1/8)`

`=tan^-1((1/2+2/5)/(1-1/2(2/5)))+tan^-1(1/8)`

`=tan^-1(7/9)+tan^-1(1/8)`

`=tan^-1((7/9+1/8)/(1-7/9(1/8)))`

`=tan^-1((65/72)/(65/72))`

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