Find the value of `4 tan^-1 (1/5) - tan^-1 (1/239) `

Explanation

Here, we will use the following properties,

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

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


Now, `4tan^(-1)(1/5) = 2(tan^(-1)(1/5)+tan^(-1)(1/5))`

`=2(tan^(-1)((2/5)/(1-1/25)))`

`=2(tan^(-1)(5/12))`

`=tan^(-1)(5/12)+tan^(-1)(5/12)`

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