Question

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

Answer 1

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