sina=-4/5 a属于(π/2.3π/2)求cos(a/2+π/3)=,

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  • 解方程组:sina=2sin(a/2)cos(a/2)=-4/5,sin(a/2)^2+cos(a/2)^2=1,构成:(sin(a/2)+cos(a/2))^2=1-4/5=1/5,

    (sin(a/2)-cos(a/2))^2=1-(-4/5)=9/5,开方:因为a属于(π/2.3π/2),所以a/2属于(π/4.3π/4),此时sin(a/2)>cos(a/2),且(sin(a/2)+cos(a/2))>0,所以::sin(a/2)+cos(a/2)=√5/5,sin(a/2)-cos(a/2)=3√5/5,解得sin(a/2)=2√5/5,cos(a/2)=-√5/5,cos(a/2+π/3)=cos(a/2)cos(π/3)-,sin(a/2)sin(π/3)=(-√5/5)*1/2-(2√5/5)*(√3/2)=-(√5+2√15)/10.