SOLUTION: How should i solve: sin(x/2)= sqrt(3) -sin(x/2) Thanks in advance!

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Question 1008826: How should i solve: sin(x/2)= sqrt(3) -sin(x/2)
Thanks in advance!
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!
How about start with combining like-terms?

One good reference solution for quadrant 1, is x=60 degrees.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Number Statement Explanation
1 sin(x/2) = sqrt(3) - sin(x/2) NA (given equation)
2 sin(x/2) + sin(x/2) = sqrt(3) - sin(x/2) + sin(x/2) Add sin(x/2) to both sides
3 2*sin(x/2) = sqrt(3) Combine like terms
4 sin(x/2) = sqrt(3)/2 Divide both sides by 2
5 x/2 = pi/3+2pi*n or x/2 = 2pi/3+2pi*n Use the unit circle (n is any integer)
6 x = 2pi/3+4pi*n or x = 4pi/3+4pi*n Multiply both sides of each equation by 2