tanx=sinx/cosx cos^2=1/1+tan 推倒已知tanx=sinx/cosx 推倒cos^2=1/1+tan^2 其中x为钝角

tanx=sinx/cosx cos^2=1/1+tan 推倒
已知tanx=sinx/cosx 推倒cos^2=1/1+tan^2 其中x为钝角

1+tan^2x
=1+sin^2x/cos^2
=cos^2x/cos^2x+sin^2/cos^2x
=(cos^2x+sin^2x)/cos^2
1/1+tan^2x
=1/[(cos^2x+sin^2x)/cos^2x]
=cos^2x/cos^2x+sin^2x
因为cos^2x+sin^2x=1
所以cos^2x/cos^2x+sin^2x=cos^2
即cos^2=1/1+tan^2