已知sin(a+π/3)-sina=3/5,-π/2<a<0,求cosa的值

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已知sin(a+π/3)-sina=3/5,-π/2<a<0,求cosa的值

已知sin(a+π/3)-sina=3/5,-π/2<a<0,求cosa的值
已知sin(a+π/3)-sina=3/5,-π/2<a<0,求cosa的值

已知sin(a+π/3)-sina=3/5,-π/2<a<0,求cosa的值
sinacosπ/3+cosasinπ/3-sina=3/5
(1/2)sina+(√3/2)cosa=3/5
sina=2[3/5-(√3/2)cosa]
(sina)^2+(cosa)^2=1
4(9/25-3√3cosa/5+3cos^2a/4)+cos^2a=1
4cos^2a-12√3cosa/5+11/25=0
100cos^2a-60√3cosa+11=0
-π/2<a<0
cos=(60√3+80)/200=(3√3+4)/10
cos=(60√3-80)/200=(3√3-4)/10

(3√5+4)/10或
(3√5-4)/10