Answer :

We are given with,

tan-1 3 + tan-1 x = tan-1 8


We need to find the value of x.


Using property of inverse trigonometry,



Let us replace A by 3 and B by x.




Since, according to the question


tan-1 3 + tan-1 x = tan-1 8


So,



Taking tangent on both sides,



Using property of inverse trigonometry,


tan(tan-1 A) = A



Now, in order to find x, we need to solve the linear equation.


By cross-multiplying,


3 + x = 8(1 – 3x)


3 + x = 8 – 24x


24x + x = 8 – 3


25x = 5



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