Prove that sineAsine2A=0.5sine2A

Answer 1

Did you mean prove: sinAsin(2A) = (1/2)sin(2A) ?

if so, then it is not true, just pick any value of A, let A = 40°
LS = sin40 * sin80 = appr .633
RS = (1/2)sin80 = .4924 , LS ≠ RS

Answer 2

however, if you want to solve
sinA sin2A = 1/2 sin2A (sin2A ≠ 0)
sinA = 1/2
A = 30°