sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).
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![sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).](/uploads/image/z/1730125-37-5.jpg?t=sina%2Bsinb%3D1%2F4%2Ccosa%2Bcosb%3D1%2F3.%E6%B1%82sin%28a%2Bb%29%2Ccos%28a-b%29.sina%2Bsinb%3D1%2F4%2Ccosa%2Bcosb%3D1%2F3.%E6%B1%82sin%28a%2Bb%29%2Ccos%28a-b%29.)
sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).
sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).
sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).
sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).sina+sinb=1/4,cosa+cosb=1/3.求sin(a+b),cos(a-b).
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]=1/4;
cosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]=1/3;
上下两式相除,得
tan[(a+b)/2]=3/4;
sin(a+b)=2sin[(a+b)/2]cos[(a+b)/2]
=2sin[(a+b)/2]cos[(a+b)/2]/{sin[(a+b)/2]^2+cos[(a+b)/2]^2}
=2tan[(a+b)/2]/(tan[(a+b)/2]^2+1)
=2*3/4/[(3/4)^2+1]
=24/25
(sina+sinb)^2=(sina)^2+(sinb)^2+2*sinasinb=1/16
(cosa+cosb)^2=(cosa)^2+(cosb)^2+2*cosacosb=1/9
以上两式相加,得1+1+2*(cosacosb+sinasinb)=25/144
cos(a-b)=cosacosb+sinasinb=-263/288