证明：(1+2sinXcosX)/(sin^2X-cos^2X)=(tanX+1)/(tanX-1)
问题描述：
证明：(1+2sinXcosX)/(sin^2X-cos^2X)=(tanX+1)/(tanX-1)
答
左=(两边同除cos^2 x) (2tanx-tan^2 x+1)/(1-tan^2 x)
=(tanx-1)^2/(tanx+1)(tanx-1)
=(tan-1)/(tanx+1)=右
答
左边=(sin²x+cos²x+2sinxcosx)/(sinx+cosx)(sinx-cosx)
=(sinx+cosx)²/(sinx+cosx)(sinx-cosx)
=(sinx+cosx)/(sinx-cosx)
分子分母同除以cosx
=(sinx/cosx+1)/(sinx/cosx-1)
=(tanx+1)/(tanx-1)
=右边
命题得证