高1数学````
∵360k+90<A<360k+180(度省略,以下相同)
∴180k+45<A/2<180k+90 即sin(a/2)>cos(a/2)
∵[cos(A/2)+sin(A/2)]^2=1+2sin(A/2)cos(A/2)=[-(根号5)/2]^2=5/4
∴2sin(A/2)cos(A/2)=1/4
∴[sin(A/2)-cos(A/2)]^2=1-2sin(A/2)cos(A/2)=3/4
∵sin(A/2)>cos(A/2)
∴sin(A/2)-cos(A/2)=(√3)/2
2sin(A/2)cos(A/2)=1/4=sinA
即sinA=1/4,则cosA=(-√15)/4
...全部
∵360k+90<A<360k+180(度省略,以下相同)
∴180k+45<A/2<180k+90 即sin(a/2)>cos(a/2)
∵[cos(A/2)+sin(A/2)]^2=1+2sin(A/2)cos(A/2)=[-(根号5)/2]^2=5/4
∴2sin(A/2)cos(A/2)=1/4
∴[sin(A/2)-cos(A/2)]^2=1-2sin(A/2)cos(A/2)=3/4
∵sin(A/2)>cos(A/2)
∴sin(A/2)-cos(A/2)=(√3)/2
2sin(A/2)cos(A/2)=1/4=sinA
即sinA=1/4,则cosA=(-√15)/4
cos2A+sin2A=(1-sinA^2)+2sinAcosA=[7-(√15)]/8
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