设cos2a=1/2 则cos^4a+sin^4a=

设cos2a=1/2 则cos^4a+sin^4a=
设cos2a=1/2 则cos^4a+sin^4a=

设cos2a=1/2 则cos^4a+sin^4a=
cos^4a+sin^4a=(cos^2a+sin^2a)^2-2sin^2acos^2a=1-2sin^2acos^2a
2sin^2acos^2a=1/2(2sinacosa)^2=(1/2)(sin2a)^2=(1/2)[1-(cos2a)^2]=(1/2)(3/4)=3/8
则cos^4a+sin^4a=1-3/8=5/8

满意请采纳~

6456546456456456