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Find all solutions of the equation sqrt(3)cos(x)=sin(x)+1 in the interval [0,2pi)

Been stumped on this qusetion for a while, anyone got a simple step-by-step solution?
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1 Answer

Square both sides
 
3cos2x = sin2x + 2 sin x + 1
 
Use the identity cos2x = 1 - sin2x
 
4 sin2x + 2 sin x - 2 = 0
2 sin2x + sin x - 1 = 0
(2 sin x - 1)(sin x + 1) = 0
 
sin x = 1/2 or sin x = -1
 
x = pi/6 = 30 degrees, x = 5pi/6 = 150 degrees or
x = 3pi/2 = 270 degrees

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