Sin2a+cos2b(бета)+7= спростити вираз

1) cos (pi/4 + а) cos (pi/4 - а) +(1/2) sin^2(a) = {произведение косинусов} =
(1/2)(cos(pi/4+a + pi/4 - a) + cos(pi/4+a - (pi/4-a))) + (1/2)sin^2(a) =
(1/2)(cos(pi/2) + cos(2a) + sin^2(a)) = {cos(pi/2) = 0, cos(2a) = cos^2(a) - sin^2(a)}
= (1/2)(cos^2(a) - sin^2(a) + sin^2(a)) = (1/2)cos^2(a)

2) cos(a-b) - cos(a+b) = {разность косинусов} =
-2sin( ((a-b)+(a+b))/2 )*sin( ((a-b)-(a+b))/2 ) = -2sin(a)sin(-b) = 2sin(a)sin(b)

3) cos(3a) + sin(a)sin(2a) = cos(3a) + (1/2)(cos(a-2a) - cos(a+2a)) =
cos(3a) + (1/2)cos(a) - (1/2)cos(3a) = (1/2)(cos(3a)+cos(a)) = {сумма косинусов}
= cos((3a+a)/2)cos((3a-a)/2) = cos(2a)cos(a)

4) cos(2a) - cos(a)cos(3a) = cos(2a) - (1/2)(cos(4a)+cos(2a)) = (1/2)(cos(2a)-cos(4a)) =
(1/2)*(-2)*sin(3a)sin(-2a) = sin(3a)sin(a)