数学证明sin^2 αtan^2 α=tan^2 α-sin^2 α

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数学证明sin^2 αtan^2 α=tan^2 α-sin^2 α
数学证明sin^2 αtan^2 α=tan^2 α-sin^2 α

数学证明sin^2 αtan^2 α=tan^2 α-sin^2 α
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

仅供参考
sina-sinb=2sin(a-b)/2*cos(a+b)/2<2sin(a-b)/2tan(a-b)>a-b