若cos2α=-3/4,则sinα^4+cosα^4等于

α是第三象限角,tanα＞0
sinα^4+cosα^4=5/9
(sinα^2+cosα^2)^2=1
sinα^4+cosα^4+2sinα^2cosα^2=1
2sinα^2cosα^2=1-5/9=4/9
sinα^2cosα^2=2/9
sinα^2=tan^2α/(1+tan^2α)
cosα^2=1/(1+tan^2α)
sinα^2cosα^2=2/9
tan^2α/(1+tan^2α) * 1/(1+tan^2α) = 2/9
9tan^2α = 2tan^4α+4tan^2α+2
(2tan^4α-5tan^2α+2)=0
(2tan^2α-1)(tan^2α-2)=0
2tan^2α=1,或tan^2α=2
tanα＞0
tanα=根号2/2,或tanα=根号2

你题目晁错了吧
应该是
sinα^4+cosα^4
=(sina^2+cosa^2)^2-2sina^2cosa^2
=1^2-2sina^2cosa^2
=1-2sina^2cosa^2
此题配方即可做出
注意sina^2+cosa^2=1哦

cos2α=3/5
2(cosα)^2-1=3/5
2(cosα)^2=8/5
(cosα)^2=4/5
(sinα)^2=1-4/5=1/5
(cosα)^2*(sinα)^2=4/25
sinα^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