Question 310853
Solve the trig equation sin(2x) = sqrt(3)sin(x)


sin(2x) = 2 sin(x) cos(x)


So we have

2 sin(x) cos(x) = sqrt(3) sin(x)


We can cancel sin(x) from both sides which makes sin(x) = 0 a solution i.e. 0, 180, 360, etc.

2 cos(x) = sqrt(3) or cos(x) = sqrt(3)/2 giving x=30 and 330.


So solutions in degrees in the range 0<=x<360 are

0, 30, 180 and 330

which shows there are four solutions for each 360 degrees range.


N.B. bear in mind that a 360 degree range does not take both end points in its range since one end point is the other end point with 360 added to it.