cos(a-b)=cosacosb+sinasinb
cosa=(-12/13), sinа=5/13, sinb=4/5, cosb=-3/5
cos(a-b)=cosacosb+sinasinb=(-12/13)*(-3/5)+(5/13)*(4/5)=56/65
Объяснение:
5/4 и 3/2 = (3 * 2) /(2 * 2) = 6/4; б) 2/3 = (2 * 5)/(3 * 5) = 10/15 и 2/15 в) 7/15 = (7 * 3)/(15 * 3) = 21/45 и 5/9 = (5 * 5)/(9 * 5) = 25/45; г) 1/6 = (1 * 5)/(6 * 5) = 6/30 и 3/10 = (3 * 3)/(10 * 3) = 9/30; д) 1/3 = (1 * 6)/(3 * 6) = 6/18 и 5/18 е) 5/8 = (5 * 3)/(8 * 3) = 15/24 и 2/3 = (2 * 8)/(3 * 8) = 16/24; ж) 1/2 = (1 * 15)/(2 * 15) = 15/30 и 2/15 = (2 * 2)/(15 * 2) = 4/30; з) 5/12 = (5 * 5)/(12 * 5) = 25/60 и 7/15 = (7 * 2)/(15 * 2) = 14/30; и) 3/10 = (3 * 10)/(10 * 10) = 30/100 и 33/100.
cos(a-b)=cos a*cos b+sin a*sin b
Пользуемся формулой (sin a)^2+(cos a)^2=1 и учитываем знак функции (углы во второй четверти)
(cos b)^2=(1-16/25)=9/25
cos b=-3/5
(sin a)^2=(1-144/169)=25/169
sin a=5/13
cos(a-b)=(-12/13)*(-3/5)+(5/13)*(4/5)=56/65