求证:(1/sin2θ)+(1/tan2θ)+(1/sinθ)=(1/(tanθ/2))
问题描述:
求证:(1/sin2θ)+(1/tan2θ)+(1/sinθ)=(1/(tanθ/2))
答
左边=1/sin2θ+cos2θ/sin2θ+1/sinθ=1/sin2θ+(2cos²θ-1)/sin2θ+1/sinθ=2cos²θ/(2sinθcosθ)+1/sinθ=(cosθ+1)/sinθ=[2cos²(θ/2)-1+1]/[2sin(θ/2)cos((θ/2)]=2cos²(θ/2)/[2sin(θ/...