若cos2α=3/5,则sinα^4+cosα^4等于
问题描述：
若cos2α=3/5,则sinα^4+cosα^4等于
答
cos2α=3/52(cosα)^2-1=3/52(cosα)^2=8/5(cosα)^2=4/5(sinα)^2=1-4/5=1/5(cosα)^2*(sinα)^2=4/25sinα^4+cosα^4=［(sinα)^2+(cosα)^2］^2-2(sinα)^2(cosα)^2=1-2(sinα)^2(cosα)^2=1-2*4/25=17/25