数学证明sin^2 αtan^2 α=tan^2 α-sin^2 α
问题描述：
数学证明sin^2 αtan^2 α=tan^2 α-sin^2 α
答
仅供参考
sina-sinb=2sin(a-b)/2*cos(a+b)/2tan(a-b)>a-b
答
左边=sin^2 αtan^2 α=sin^2 α*(sin^2 α/cos^2α)=sin^4α/cos^2α
右边=tan^2 α-sin^2 α=(sin^2 α/cos^2α)-sin^2 α=(sin^2 α/cos^2α)-(sin^4/cos^2α)=(sin^2α-sin^4α)/cos^2α=sin^2α(1-cos^2α)/cos^2α=sin^4α/cos^2α=左边