Solve the following for `x :` `tan^(-1)2x+tan^(-1)3x=npi+(3pi)/4`

Explanation

`tan^(-1)2x+tan^(-1)3x=pi/4`
`rArrtan^(-1)((2x+3x)/(1-6x^2))=pi/4 " only if "(2x)(3x) lt 1`
`rArr tan^(-1)((5x)/(1-6x^2))=pi/4 "i.e.,"6x^2 lt 1`
`(5x)/(1-6x^2)=pi/4` `:.x in((-1)/sqrt6),1/sqrt6)`
=1
`rArr 5x=1-6x^2`
`rArr 6x^2-5x-1=0`
`rArr(6x-1)(x+1)=0`
`x=-1 or x=1/6`
But x = -1 does not lie in domain of x therefore `x=1/6`