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

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

1.	Solve the following equation for `x :``tan^(-1)(1/4)+2tan^(-1)(1/5)+tan^(-1)(1/6)+tan^(-1)(1/x)=pi/4`
Answer» `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` `tan^-1 (1/x) = tan^-1 1 - tan^-1(235/226)` `= tan^-1((1- 235/226)/(1 + 235/226))` `tan^-1 (1/x) = tan^-1((226-235)/(226 + 235))` `1/x = -9/461` `x= -461/9` Answer

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