How do you solve for x? Sin x = Sin (2x - π) XE [0, 2π]

Question

722 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-30T01:48:16

See below

#Sin x = Sin (2x - π)#

Apply sine difference identity:
#sinx= sin2xcospi-cos2xsinpi#

#sinx= sin2x(-1)-cos2x(0)#

#sinx=-sin2x#

#sinx+sin2x=0#

Apply sin double angle identity:
#sinx+2sinxcosx=0#
#sinx(1+2cosx)=0#

#sinx=0#
#x=pi, 0, 2pi#

#cosx=-1/2#
#x=(2pi)/3, (4pi)/3#

graph{sinx-sin(2x-pi) [-10, 10, -5, 5]}