Solve the following equation for `x :` `tan^(-1)(1/4)+2tan^(-1)(1/5)+tan^(-1)(1/6)+tan^(-1)(1/x)=pi/4`

Explanation

`2 tan^-1 x = tan^-1((2x)/(1-x^2))`

now,`tan^-1 (1/4) + tan^-1((2/5)/(1-(1/25))) + tan^-1(1/6) + tan^-1 (1/x) = pi/4`

=`tan^-1(1/4) + tan^-1(5/12) + tan^-1(1/6) + tan^-1(1/x) = tan^-1 1`

`= tan^-1((1/4 + 5/12)/(1- 5/48)) + tan^-1(1/6) + tan^-1 (1/x) = tan^-1 1`

`= tan^-1(32/43) + tan^-1(1/6) + tan^-1(1/x) = tan^-1(1) `

`= tan^-1((32/43 + 1/6)/(1- (32/43)(1/6))) + tan^-1(1/x) = tan^-1 1`

`= tan^-1(((192+43)/258)/((258- 32)/(258))) + tan^-1 (1/x)= tan^-1 1 `

`tan^-1 (235/226) + tan^-1(1/x) = tan^-1 1`

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