三倍角公式的可视化证明

$sin3\theta=sin\theta+2sin\theta cos2\theta=sin\theta+2sin(1-sin^2\theta)=sin\theta+2sin\theta-4sin^3\theta=3sin\theta-4sin^3\theta$

$cos3\theta=2cos2\theta cos\theta-cos\theta=2cos\theta(2sin^2\theta-1)-cos\theta=4cos^3\theta-2cos\theta-cos\theta=4cos^3\theta-3cos\theta$