Б) формула сумма косинусов...
...= 2*cos((a+b)/2)*cos((a-b)/2) = 2*cos(2pi)*cos(pi/4) = 2*1*√2 / 2 = √2
в) можно выделить полный квадрат...
(sin(a))^4 + (cos(a))^4 + 2*(sin(a))^2*(cos(a))^2 - 2*(sin(a))^2*(cos(a))^2 =
((sin(a))^2 + (cos(a))^2)^2 - 2*(sin(a))^2*(cos(a))^2 =
1 - 2*(sin(a))^2*(cos(a))^2 = 1 - 2*1/16 = 1 - 1/8 = 7/8
(sina + cosa)^2 = 1/2
(sin(a))^2 + (cos(a))^2 + 2*sina*cosa = 1/2
2*sina*cosa = 1/2 - 1 = -1/2
sina*cosa = -1/4
(sina*cosa)^2 = 1/16