SOLUTION: solve the equation in radians for all exact solutions. 2sqrt( 3 )cos(x/2)=-3

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Question 682511: solve the equation in radians for all exact solutions.
2sqrt( 3 )cos(x/2)=-3
Answer by lwsshak3(11628) About Me  (Show Source):
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solve the equation in radians for all exact solutions.
2sqrt( 3 )cos(x/2)=-3
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2√3cos(x/2)=-3
cos(x/2)=-3/(2√3)
Identity: cos(x/2)=±√[(1+cos x)/2]
±√[(1+cos x)/2]=-3/(2√3)
square both sides
(1+cos x)/2=9/12
1+cos x=18/12=3/2
cos x=3/2-1=1/2
x=π/3+2πk, 5π/3+2πk, k=integer