SOLUTION: Solve : sin2x=sinx

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Question 1189408: Solve : sin2x=sinx
Answer by MathLover1(20850) About Me  (Show Source):
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sin%282x%29=sin%28x%29...........use Double-Angle Identities sin%282x%29=+2sin%28x%29cos+%28x%29
2sin%28x%29cos+%28x%29=sin%28x%29
2sin%28x%29cos+%28x%29-sin%28x%29=0
sin%28x%29%282cos+%28x%29-1%29=0

solutions:
if sin%28x%29=0+
x=sin%5E-1%280%29
x=2pi%2An
x=pi%2B2pi%2An

if 2cos+%28x%29-1=0 ->2cos+%28x%29=1->cos+%28x%29=1%2F2
x=cos%5E-1%281%2F2%29
x=pi%2F3%2B2pi%2An
x=5pi%2F3%2B2pi%2An
combine solutions:
x=2pi%2An, x=pi%2B2pi%2An, x=pi%2F3%2B2pi%2An, x=5pi%2F3%2B2pi%2An