3+cos4a-4cos2a=8sin^4(a) 求证.谁会?、

左边=2cos²2a-4cos2a+2
=2(cos²2a-2cos2a+1)
=2(cos2a-1)²
=2(1-2sin²a-1)²
=2*4sin⁴a
=8sin⁴a=右边
∴等式得证

cos(2a)=1-sin^2(a)
cos(4a)=1-2sin^2(2a)
=1-8sin^2(a)cos^2(a)
原式=8sin^2(a)(1-cos^2(a))=8sin^4(a)