How do you solve $(1-tan^2x)tan2x=2sqrt3$ ?

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Answer 1 · 2016-08-01T13:37:58

$tan x=sqrt3$

$color(red)((1-tan^2 x))tan 2x=2sqrt3 ?$

$tan (a+b)=(tan a+tan b)/(1-tan a*tan b)$

$tan (x+x)=tan(2x)=(tan x+tan x)/(1-tan x*tan x)$

$tan 2x=(2tan x)/(1-tan^2 x)$

$color(red)(1-tan^2 x)=(2 tan x)/(tan 2x)$

$"let us write the equation again"$

$((2 tan x)/cancel((tan 2x)))cancel(tan 2x)=2sqrt3$

$"yields :"$

$cancel(2) tan x=cancel(2) sqrt 3$

$tan x=sqrt3$

How do you solve (1-tan^2x)tan2x=2sqrt3(1-tan^2x)tan2x=2sqrt3?