SOLUTION: find all solutions of the equation on the interval [0, 2pie). - square root 3 cos x + sin x = -square root 3

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Question 944798: find all solutions of the equation on the interval [0, 2pie). - square root 3 cos x + sin x = -square root 3
Answer by lwsshak3(11628) About Me  (Show Source):
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find all solutions of the equation on the interval [0, 2pie). - square root 3 cos x + sin x = -square root 3
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sqrt%283%29cosx%2Bsinx=-sqrt%283%29
sqrt%283%29cosx%2Bsqrt%283%29=-sinx
sqrt%283%29%28cosx%2B1%29=-sinx
square both sides:
3(cos^2(x)+2cosx+1)=sin^2(x)
3cos^2(x)+6cosx+3=1-cos^2(x)
4cos^2(x)+6cosx+2=0
2cos^2(x)+3cosx+1=0
(2cosx+1)(cosx+1)=0
..
2cosx+1=0
cosx=-1/2
x=2π/3, 4π/3
..
cosx+1=0
cosx=-1
x=π