字典翻译 问答 小学 数学 已知cos(θ+π/2)=-1/2,求值已知cos(θ+π/2)=-1/2,求cos(θ+π)/sin(π/2-θ)[cos(3π-θ)-1]+cos(θ-2π)/cos(-θ)*cos(π-θ)+sin(θ+5π/2)的值
问题标题:
已知cos(θ+π/2)=-1/2,求值已知cos(θ+π/2)=-1/2,求cos(θ+π)/sin(π/2-θ)[cos(3π-θ)-1]+cos(θ-2π)/cos(-θ)*cos(π-θ)+sin(θ+5π/2)的值
问题描述:

已知cos(θ+π/2)=-1/2,求值

已知cos(θ+π/2)=-1/2,求cos(θ+π)/sin(π/2-θ)[cos(3π-θ)-1]+cos(θ-2π)/cos(-θ)*cos(π-θ)+sin(θ+5π/2)的值

潘嘉林回答:
  cos(θ+π)/sin(π/2-θ)[cos(3π-θ)-1]+cos(θ-2π)/cos(-θ)*cos(π-θ)+sin(θ+5π/2)   =   (-cosθ)/(cosθ)[-cosθ-1]+(cosθ/cosθ)*(-cosθ)+cosθ   =cosθ+1+(-cosθ)+cosθ   =cosθ+1   =√3/2+1或=-√3/2+1   cos(θ+π/2)=-1/2   sinθ=cos(π/2-θ)=1/2,cosθ=√3/2或cosθ=-√3/2
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