Let theta be an acute angle such that sin 2 theta = sin 3 theta + sin theta. What is the measure of theta in degrees?
+130077 2sinxcosx = sin (2x)cosx + sinxcos(2x) + sin x
2sin x cos x = 2sinxcos^2x + sinx (cos^2x - sin^2x) + sinx
2sinx cos x = 3sinxcos^2x - sin ^3 x +sin x
Since sin x not = 0 , divide through by sin x
2cosx = 3cos^2x - sin^2x + 1
2cosx = 3cos^2x - (1 - cos ^2x) + 1
2cos x = 4cos^2 x
4cos^2x - 2cos x = 0
2cos x ( 2cos x - 1) = 0
2cos x = 0
cos x = 0
x = 90° (not acute)
2cos x -1 = 0
2cos x = 1
cos x = 1/2
x = 60° = theta
