#3sin^2x# = 2𝑠𝑖𝑛𝑥𝑐𝑜𝑠𝑥 is this a provable? if not, solve the equation for -180 < 𝑥 < 180?

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Answer 1 · 2018-02-26T00:15:35

#-116.57^@, 0^@,63.43^@#

#3sin^2x=2sinxcosx#

Let #x=60^@#

#3sin^2(60^@)=2sin(60^@)cos(60^@)#

#3/4=2(sqrt(3)/2)(1/2)#

#3/4=sqrt(3)/2color(white)(888)#False not an identity.

Solution:

#3sin^2x-2sinxcosx=0#

#sinx(sinx-2cosx)=0#

#sinx=0#

#x=arcsin(sinx)=arcsin(0)=>x=0^@,#

#sinx-2cosx=0#

#-2cosx=-sinx#

#2=sinx/cosx#

Identity.

#color(red)bb(sinx/cosx=tanx)#

#tanx=2#

#x=arctan(tanx)=arctan(2)=>x=arctan(2),arctan(2)-180^@#

#arctan(2)~~63.43^@#

#arctan(2)-180^@~~-116.57^@#