已知cosa-cosb=1/3,sin-sinb=1/2.求cos(a-b)的值 化简:cos^2(a+45度)-sin

cosa-cosb=1/3 (1)
sina-sinb=1/2 (2)
(1)两边平方得
cos²a-2cosacosb+cos²b=1/9 (3)
(2)两边平方得
sin²a-2sinacosa+sin²b=1/4 (4)
(3)+(4)得
2-2(cosacosb+sinasinb)=13/36
-2cos(a-b)=-59/36
∴cos(a-b)=59/72

2、cos^2(a+45度)-sin^2(a+45度)
=(cosacos45°-sinasin45°)²-(sinacos45+cosasin45)²
=1/2(cosa-sina)²-1/2(sina+cosa)²
=2sinacosa
=sin2a

cosa-cosb=1/3
(cosa-cosb)²=1/9
cos²a+cos²b-2cosacosb=1/9..........................(1)
sin-sinb=1/2
(sina-sinb)²=1/4
sin²a+sin²b-2sinasinb=1/4.......

cosa-cosb=1/3,
cos^2a-2cosacosb+cos^2b=1/9.....(1)
sina-sinb=1/2.
sin^2a-2sinasinb+sin^2b=1/4........(2)
.(1)+.(2)得
2-2(cosacosb+sinasinb)=13/36
cosacosb+sinasinb=-59/72
co...

(1)
因为cosB=4/5
所以sinB=√(1-16/25)=3/5
因为AB=AC
所以∠C=∠B
所以∠A=180°-2∠B
cosA=cos（180°-2∠B）=-cos（2∠B）=sin²B-cos²B=9/25-16/25=-7/25
(2)
sinA=√(1-49/625)=24/25
ta...