已知sinθ/2+cosθ/2=2√3/3,求sinθ,cos2θ
问题描述：
已知sinθ/2+cosθ/2=2√3/3,求sinθ,cos2θ
答
sinθ/2+cosθ/2=2√3/3
sinθ=2sinθ/2cosθ/2=(sinθ/2+cosθ/2)²-1=4/3-1=1/3
sin²θ=1/9
cos2θ=(1-2sin²θ)=1-2/9=7/9
答
sinθ/2+cosθ/2=2√3/3
两边平方
sin²θ/2+cos²θ/2+2sinθ/2cosθ/2=4/3
1+sinθ=4/3
sinθ=1/3
cos2θ
=1-2sin²θ
=7/9