求证:(sin 2x /(1-cos 2x) )·(sin x /(1+sin x))=tan (π/4-x/2).
问题描述:
求证:(sin 2x /(1-cos 2x) )·(sin x /(1+sin x))=tan (π/4-x/2).
答
[sin 2x /(1-cos 2x)]·[sin x /(1+sin x)]=2sinx*cosx*sinx/[2(sinx)^2*(1+sinx)]=cosx/(1+sinx)=[(cosx/2)^2-(sinx/2)^2]/[(cosx/2)^2+(sinx/2)^2+2cosx/2*sinx/2]=[(cosx/2+sinx/2)*(cosx/2-sinx/2)]/[(cosx/2+si...