已知cos(a+b)cos(π/4 -b)-sin(a+b)sin(π/4 -b)=-4/5,且π/4

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已知cos(a+b)cos(π/4 -b)-sin(a+b)sin(π/4 -b)=-4/5,且π/4
已知cos(a+b)cos(π/4 -b)-sin(a+b)sin(π/4 -b)=-4/5,且π/4

已知cos(a+b)cos(π/4 -b)-sin(a+b)sin(π/4 -b)=-4/5,且π/4
cos(a+b)cos(π/4 -b)-sin(a+b)sin(π/4 -b)
=cos[(a+b)+(π/4-b)]
=cos(a+π/4)=-4/5
cosacosπ/4-sinasinπ/4=-4/5
cosa-sina=-4√2/5
两边平方
cos²a+cos²a-2sinacosa=32/25
1-2sinacosa=32/25
sin2a=2sinacosa=-7/25
sina-cosa=4√2/5
-sinacosa=7/50
即sina+(-cosa)=4√2/5
sina*(-cosa)=7/50
所以sina和-cosa是方程x²-4√2x/5+7/50=0的根
(x-√2/5)(x-7√2/5)=0
x=√2/5,x=7√2/5
π/4