若sinθ×cosθ=1/3,则sin四次方α+cos四次方α的值是?

问题描述:

若sinθ×cosθ=1/3,则sin四次方α+cos四次方α的值是?

sinθcosθ=1/3
(sin^2θ+cos^2θ)^2=1
sin^4θ+cos^4θ+2sin^2θcos^2θ=1
sin^4θ+cos^4θ=1-2sin^2θcos^2θ=1-2/9=7/9