Question

已知cos2θ=3/9,求sin4次方θ+cos4次方θ的值

详细的过程谢谢

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

Answer 2

cos2θ=3/9，sin2θ=2√2/3
sin4次方θ+cos4次方θ=sin4次方θ+cos4次方θ+2sin平方θcos平方θ-2sin平方θcos平方θ
=（sin²θ+cos²θ）-2（sinθcosθ）²
=1-2（2√2/3）²
=-7/9

Answer 3

5