cos2α=4分之5,则cos4次方α+sin4次方α=
问题描述：
cos2α=4分之5,则cos4次方α+sin4次方α=
答
cos2α=(cosα)^2-(sinα)^2=5/4
(cosα)^2+-(sinα)^2=1
则(cosα)^2=9/8 (sinα)^2=-1/8
(cosα)^4+(sinα)^4=((cosα)^2+-(sinα)^2)^2-2*(cosα)^2*(sinα)^2=1-2*(9/8)*(-1/8)=41/32
答
cos2α=2cos平方α-1=4/5,解出cos平方α=9/10,sin平方α=1/10,所以cos4次方α+sin4次方α=(9/10)的平方+(1/10)的平方=82/100=41/50