Question

x=sin^4θ+cos^4θ 就这个方程而言 x的取值为多少? 请详写步骤~

Answer 1

x=sin^4θ+cos^4θ

=(sin^2θ+cos^2θ)^2-2sin^2θcos^2θ

=1-1/2(sin2θ)^2

－1≤sin2θ≤1

0≤(sin2θ)^2≤1

1/2≤x=1-1/2(sin2θ)^2≤1