sin2a/sin(a-π/4)=-根号2/2,则sina+cosa=sin2a / sin(a-π/4)= - 根号2/2, 则sina+cosa=
问题描述：
sin2a/sin(a-π/4)=-根号2/2,则sina+cosa=
sin2a / sin(a-π/4)= - 根号2/2, 则sina+cosa=
答
sin(a)-cos(a)=√2sin(a-π/4)=√2cos(a+π/4)=-2sin(2a)
sin(a)+cos(a)=√2cos(a-π/4)=√2sin(a+π/4)
4sin(a)cos(a)=1-cos(2a+π/2)-2sin^2(2a)=1+sin(2a)-4sin^2(2a)=2sin(2a)
4sin^2(2a)+sin(2a)-1=0
sin(2a)=(-1+_√17)/8
sin(a-π/4)=(1_+√17)/4
sin(a+π/4)=-cos(2a)=懒得算
最后看看象限的范围吧