求证(sinθ+cosθ-1)(sinθ-cosθ+1)/sin2θ=tanθ/2

问题描述:

求证(sinθ+cosθ-1)(sinθ-cosθ+1)/sin2θ=tanθ/2

原式=(sinθ2-(cosθ-1)2)/sin2θ
=(2cosθ-2cosθ2)/sin2θ
=(1-cosθ)/sinθ
= ( 2cos(θ/2) )2/sinθ
=tan(θ/2)