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#