If `3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)1/x=tan^(-1)1/3,`then `x`is equal to1 (b) 2(c) 3 (d)`sqrt(2)`

If `3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)1/x=tan^(-1)1/3,`then `x`is equal

1.	If `3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)1/x=tan^(-1)1/3,`then `x`is equal to1 (b) 2(c) 3 (d)`sqrt(2)`
Answer» `3tan^-1(1/(2+sqrt3)) - tan^-1 (1/x) = tan^-1 (1/3)` `=>3tan^-1(1/(2+sqrt3)*(2-sqrt3)/(2-sqrt3)) = tan^-1 (1/x) + tan^-1 (1/3)` `=>3tan^-1(2-sqrt3) = tan^-1 (1/x) + tan^-1 (1/3)` Now, we know, `tan15^@ = 2-sqrt3=>15 = tan^-1(2-sqrt3)` `:. 315^@ = tan^-1((1/3+1/x)/(1-(1/3)(1/x)))` `=>tan45^@ = (x+3)/(3x-1)` `=>1(3x-1) = x+3` `=>2x = 4` `=> x = 2.`

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