已知cos(15°+α)=1/3,α为第一象限角,求cos(75°-α)+sin(α+105°)

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/01 01:52:17

已知cos(15°+α)=1/3,α为第一象限角,求cos(75°-α)+sin(α+105°)

∵cos(15°+α)=1/3
∴sin(α+105º)
=sin[90º+(15º+α)]
=cos(15º+α)=1/3
∵α为第一象限角
即k×360º

  cos(15°+α)=1/3,则sin(15°+α)=根号(1-1/9)=2根号2/3,
  cos(75°-α)+sin(α+105°)
  =cos(90°-(15°+α))+sin(90°+(15°+α))
  =sin(15°+α)+cos(15°+α)
  =2根号2/3+1/3