SOLUTION: What are the solutions of the equation tan(x/2)-sin(x)=0

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Question 799834: What are the solutions of the equation tan(x/2)-sin(x)=0
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given;
(1) tan(x/2) - sin(x) = 0 or
(2) tan(x/2) = sin(x)
Use the half angle idenity of the tangent function given by
(3) tan(x/2) = sin(x)/(1+cos(x))
Substitute (2) into (3) and get
(4) sin(x) = sin(x)/(1+cos(x)) or
(5) 1 = 1/(1+cos(x)) or
(6) 1+cos(x) = 1 or
(7) cos(x) = 0
(8) x = arcos(0) or
(9) x = + or - 90 and all angles + or - 180 from 90 or
Answer:+x+=%282n-1%29%2Api%2F2 where n is any integer