化简cos^4 α+sin^4 α-1/4(1+cos4α)
问题描述：
化简cos^4 α+sin^4 α-1/4(1+cos4α)
答
(sinx)^4+(cosx)^4
=[1-(cosx)^2](sinx)^2+[1-(sinx)^2](cosx)^2
=1-2(sinxcosx)^2
=1-1/2*(sin2x)^2
=3/4+1/4*cos4x
答
cos^4 α+sin^4 α-1/4(1+cos4α)
=1-2(sinαcosα)^2-(1/4)[1+1-2(sin2α)^2]
=1-(1/2)(sin2α)^2-1/2+(1/2)(sin2α)^2
=1/2