Question

已知cos2θ=3/9,求sin4次方θ+cos4次方θ的值

Answer 1

注：如cos2θ=3/9 则有：　　cos²θ-sin²θ=3/9

所以可得：cos²θ=13/18, sin²θ=7/18

sin4次方θ+cos4次方θ

=(sin²θ+cos²θ)²-2sin²θcos²θ

=1-2x7/18x13/18

=53/144

如：cos²θ=3/9 则有：sin²θ=1-3/9=6/9

sin4次方θ+cos4次方θ

=(sin²θ+cos²θ)²-2sin²θcos²θ

=1-2x3/9x6/9

=5/9