Question

高一必修二数学习题，烦高手解答求证

求证cos(π-θ)/cosθ[sin(3π/2-θ)-1]+cos(2π-θ)/cos(π+θ)sin(π/2+θ-sin(3π/2+θ)=2/sin²θ
已经很清楚了啊

Answer 1

左边=cos(π-θ)/cosθ[sin(3π/2-θ)-1]+cos(2π-θ)/cos(π+θ)[sin(π/2+θ)-1]
=-cosθ/cosθ*[-cosθ-1]+cosθ/(-cosθ)*[cosθ-1]
=1/(cosθ+1)-1/(cosθ-1)
=1/(cosθ+1)+1/(1-cosθ)
=(1-cosθ+1-cosθ)/(1-cos^2θ)
=2/(1-cos^2θ)
=2/sin²θ
=右边
感觉原题有误，改之……

Answer 2

写清楚,看不清,很简单的三角函数恒等变形