Question

1)求证cotαcosα/cotα-cosα=tan(α/2+π/4)

Answer 1

cotxcosx/(cotx-cosx)=cosx/(1-sinx)=(cos^2x/2-sin^2x/2)/(sin^2x/2+cos^2x/2+2sinx/2cosx/2)=(cos^2x/2+sin^2x/2)(cos^2x/2-sin^2x/2)/(sin^2x/2-cos^2x/2)^2=(cosx/2+sinx/2)/(cosx/2-sinx/2)=(tanx/2+1)/(1-tanx/2)=tan(x/2+派/4),得证