化简sin(A+π/4)sin(A-π/4)/sin^4A-cos^4A
问题描述：
化简sin(A+π/4)sin(A-π/4)/sin^4A-cos^4A
答
原式=cos[π/2-(A+π/4)]sin(A-π/4)/(sin²A+cos²A)(sin²A-cos²A)
=cos(π/4-A)sin(A-π/4)/1×(sin²A-cos²A)
=cos(A-π/4)sin(A-π/4)/1×(sin²A-cos²A)
=[1/2sin2(A-π/4)]/cos2A
=[1/2sin(2A-π/2)]/cos2A
=[-1/2cos2A]/cos2A
=-1/2