请教一道求值域的题~在线等

y=sin(2x-30度)cos2x的值域:-3/4≤y≤1/4

y=sin(2x-30°)cos2x
=[sin(2x-30°+2x)+sin(2x-30°-2x)]/2
=[sin(4x-30°)-sin30°]/2
=[sin(4x-30°)-1/2]/2

-1≤sin(4x-30°)≤1
y=[sin(4x-30°)-1/2]/2
4y+1=2sin(4x-30°)
sin(4x-30°)=(4y+1)/2
-1≤(4y+1)/2≤1
-3/4≤y≤1/4

积化和差sinXcosY=1/2[sin(X+Y)+sin(X-Y)]
cosXsinY=1/2[sin(X+Y)-sin(X-Y)]

用这个公式就可以了.
y=sin(2x-30度)cos2x=1/2[sin(4x-30)+sin(-30)]
而sinx 的值域应该知道吧