((1+sinθ-cosθ)/(1+sinθ-cosθ))+ cot(θ/2)

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((1+sinθ-cosθ)/(1+sinθ-cosθ))+cot(θ/2)((1+sinθ-cosθ)/(1+sinθ-cosθ))+cot(θ/2)((1+sinθ-cosθ)/(1+sinθ-c

((1+sinθ-cosθ)/(1+sinθ-cosθ))+ cot(θ/2)
((1+sinθ-cosθ)/(1+sinθ-cosθ))+ cot(θ/2)

((1+sinθ-cosθ)/(1+sinθ-cosθ))+ cot(θ/2)
(1)令t=tan (θ/2)由万能公式sinθ=(2t)/(t^2+1) cosθ=(t^2-1)/(t^2+1)原式=(t^2+1+2t-t^2+1)/(t^2+1+2t+t^2-1)=(2t+2)/(2t^2+2t)=1/t=cot (θ/2)(2)令t=tan(3a/2) tan 3a=(2t)/(1-t^2)原式=t*(2t)/(1-t^2)+1=(2t^2+1-t^2)/(1-t^2)=(1+t^2)/(1-t^2)由万能公式 (1+t^2)/(1-t^2)=-1/cos(3a)=-sec(3a)