Question

已知cos2a=（1/4),求cos^4a+sin^4+sin^2acos^2a的值

Answer 1

cos(2a)=1/4

[sin(2a)]^2=1-[cos(2a)]^2=1-1/16=15/16

(cosa)^4+(sina)^4+(sina)^2(cosa)^2

=[(cosa)^2+(sina)^2]^2-(sina)^2(cosa)^2

=1-sin(2a)^2/4

=1-(15/16)/4

=1-15/64

=49/64