百度作业网三角函数 (20 17:30:8)
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/07/11 18:41:41
三角函数 (20 17:30:8)
若[cos2a] / sin(a-π/4)=-（根号2）/2 则 sina+cosa的值
若[cos2a] / sin(a-π/4)=-（根号2）/2 则 sina+cosa的值
化简：
cos2a/sin(a-π/4)
=(2cos2a*cos(a-π/4)) /(2sin(a-π/4) cos(a-π/4))
=(2cos2a*cos(a-π/4)) /sin(2a-π/2)
=-(2cos2a*cos(a-π/4)) /cos2a
=-2*cos(a-π/4) =-√2/2
∴cos(a-π/4) =√2/4
即：
cosa*cos(π/4)+sina*sin(π/4)=√2/4
sina+cosa=1/2
cos2a/sin(a-π/4)
=(2cos2a*cos(a-π/4)) /(2sin(a-π/4) cos(a-π/4))
=(2cos2a*cos(a-π/4)) /sin(2a-π/2)
=-(2cos2a*cos(a-π/4)) /cos2a
=-2*cos(a-π/4) =-√2/2
∴cos(a-π/4) =√2/4
即：
cosa*cos(π/4)+sina*sin(π/4)=√2/4
sina+cosa=1/2