SOLUTION: Find the solutions in the interval (0,2pi) for sin2xcosx +cos2xsinx=-1/2

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Question 957599: Find the solutions in the interval (0,2pi)
for sin2xcosx +cos2xsinx=-1/2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity,
sin%28a%2Bb%29=sin%28a%29cos%28b%29%2Bcos%28a%29sin%28b%29
.
.
sin%282x%29cos%28x%29%2Bcos%282x%29sin%28x%29=sin%282x%2Bx%29=sin%283x%29
sin%283x%29=-1%2F2
So,
3x=%287%2F6%29pi and 3x=%2811%2F6%29pi
x=%287%2F18%29pi and x=%2811%2F18%29pi