Solve for x, `tan^(-1)2x+tan^(-1)3x=pi/4`

1.	Solve for x, `tan^(-1)2x+tan^(-1)3x=pi/4`
Answer» `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`

Discussion

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