Question 1072633: Solve sin(2x) = sin(x/2) pls.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! sin(2x) = sin(x/2)
2sin(x)cos(x) = sin(x/2)
2*(2sin(x/2)cos(x/2))*(1 - 2sin^2(x/2)) = sin(x/2)
Sub t for x/2
4sin(t)cos(t) - 8sin^3(t)cos(t) - sin(t) = 0
--> sin(x/2) = 0 is a root
--> x = 0
===========================
4cos(t) -8sin^2(t)cos(t) - 1 = 0
4cos(t) -8(1-cos^2(t))*cos(t) - 1 = 0
4cos(t) -8 + 8cos^3(t) - 1 = 0
8cos^3 + 4cos - 9 = 0
===========================
I get roots at 2pi/5 and 6pi/5 graphically, but something's wrong, it doesn't match the calculations.
I'll work on it later today.
|
|
|
