己知sin^2θ=sinα cosα 求cos2θ=2sin(45°-α) cos(45°+α) 急!~~
问题描述：
己知sin^2θ=sinα cosα 求cos2θ=2sin(45°-α) cos(45°+α) 急!~~
答
证明：∵ 2sin(45°-α) cos(45°+α)=2sin(45°-α) cos[90°-(45°-α)]=2sin(45°-α) sin(45°-α)=2sin²(45°-α)=1-cos(90°-2α)=1-sin2α=1-2sinαcosα=1-2sin²θ=cos2θ∴ cos2θ=2sin(45°-α)...