已知COS2α=1/4,则COS^4+SIN^4+SIN^2αCOS^2α的值等于

题目

已知COS2α=1/4,则COS^4+SIN^4+SIN^2αCOS^2α的值等于

答案

COS^4+SIN^4+SIN^2αCOS^2α
=（sin^2α+cos^2α)^2-sin^2αcos^2α
=1-（1/2sin2α)^2
=1-1/4 (sin2α)^2
=1-1/4 {1-(cos2α)^2}
=1-1/4{1-(1/4)^2}
=1-1/4*15/16
=49/64