sin(a+b)=-3/5,sin(b-π/4)=12/13,求cos(a+π/4)值
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sin(a+b)=-3/5,sin(b-π/4)=12/13,求cos(a+π/4)值
cos(a+π/4)
=cos[(a+b)-(b-π/4)]
=cos(a+b)cos(b-π/4)+sin(a+b)sin(b-π/4)
又sin(a+b)=-3/5,sin(b-π/4)=12/13,
所以cos(a+b)=4/5(a+b为第四象限角),cos(a+b)=4/5(a+b为第四象限角)
cos(b-π/4)=5/13(b-π/4为第一象限角),cos(b-π/4)=-5/13(b-π/4为第二象限角),
所以cos(a+π/4)=-16/65,-56/65
=cos[(a+b)-(b-π/4)]
=cos(a+b)cos(b-π/4)+sin(a+b)sin(b-π/4)
又sin(a+b)=-3/5,sin(b-π/4)=12/13,
所以cos(a+b)=4/5(a+b为第四象限角),cos(a+b)=4/5(a+b为第四象限角)
cos(b-π/4)=5/13(b-π/4为第一象限角),cos(b-π/4)=-5/13(b-π/4为第二象限角),
所以cos(a+π/4)=-16/65,-56/65
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