求证1+2sinαcosα/sin^2α-cos^2α=tanα+1/tanα-1
问题描述:
求证1+2sinαcosα/sin^2α-cos^2α=tanα+1/tanα-1
答
左边=(sin²α+cos²α-2sinαcosα)/(sinα+cosα)(sinα-cosα)=(sin+cosα)²/(sinα+cosα)(sinα-cosα)=(sin+cosα)/(sinα-cosα)上下除以cosα由sinα/cosα=tanα所以左边=(tanα+1)/(tanα-1)...