How can i solve this equation : #tan(45+x)-3tan x=2# ?

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Answer 1 · 2018-01-20T03:52:30

#tan(45+x)-3tanx=2#

#=>(tan45+tanx)/(1-tan45tanx)+1=3(1+tanx)#

#=>(1+tanx)/(1-tanx)+1=3(1+tanx)#

#=>2/(1-tanx)=3(1+tanx)#

#=>2/3=(1-tan^2x)#

#=>tan^2x=1-2/3=1/3#

#=>tanx=pm1/sqrt3=pmtan(pi/6)#

#=>x=npipmpi/6" where " ninZZ#