已知sin(α-3π/4)cos(α-π/4)=-1/4,求cos4α
【解】sin(α-3π/4)= sin[(α-π/4) -π/2]
=- sin[π/2- (α-π/4)]
=-cos(α-π/4).
因为sin(α-3π/4)cos(α-π/4)=-1/4,
所以-cos(α-π/4) cos(α-π/4)=-1/4,
cos²(α-π/4) =1/4,
[1+ cos2(α-π/4)]/2 =1/4,
1+cos(2α-π/2) =1/2,
sin(2α) =-1/2,
cos4α=1-2 sin² (2α)=1/2.