Если правильно разглядела, под таким углом снято, конечно...
1) sin(pi/6 - a) - cos(pi/3 + a) = sin(pi/6)*cosa - cos(pi/6)*sina - cosa*cos(pi/3) + sina*sin(pi/3) = 0.5*cosa - sqrt3*sina/2 - 0.5*cosa + sqrt3*sina/2 = 0
2) а) sin9x*cos3x - cos9x*sin3x = 2/5
sin(9x - 3x) = 2/5
sin6x = 2/5
6x = ((-1)^k)*arcsin(2/5) + pi*k
x = (1/6)*((-1)^k)*arcsin(2/5) + pi*k/6
б) sinx + cosx = 1
sin(2*x/2) = 2*sin(x/2)*cos(x/2)
cos(2*x/2) = cos^2(x/2) - sin^2(x/2)
2*sin(x/2)*cos(x/2) + cos^2(x/2) - sin^2(x/2) = sin^2(x/2) + cos^2(x/2)
2*sin(x/2)*cos(x/2) - 2sin^2(x/2) = 0
sin(x/2) * (cos(x/2) - sin(x/2)) = 0
sin(x/2) = 0, x/2 = pi*k, x=2pi*k
sin(x/2) = cos(x/2), tg(x/2) = 1, x/2 = +- pi/4 + pi*k, x = +- pi/2 + 2pi*k