sec^2 x-1 =tan^2 x 怎么来的啊

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sec^2 x-1 =tan^2 x 怎么来的啊
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sec^2 x-1 =tan^2 x 怎么来的啊
sec^2 x-1 =tan^2 x 怎么来的啊

sec^2 x-1 =tan^2 x 怎么来的啊
tan²x=(sin²x)/(cos²)=(1-cos²)/(cos²)=(1/cos²x)-(cos²)/(cos²)=sec²x-1.

[sec^2 x]-1=[1/cos^2 x]-1
=(1-cos^2 x)/cos^2x
=sin^2 x/cos^2 x
=tan^2 x

sin²x+cos²x=1
(sinx/cosx)²+(cosx/cosx)²=(1/cosx)²
tan²x+1=sec²x