sin(x/2)*sin(3x/2*pi/4)

Solution for sin(x/2)*sin(3x/2*pi/4) equation:

x in (-oo:+oo)

sin(x/2)*sin((pi*((3*x)/2))/4) = 0

sin(x/2) = 0

sin(x/2) = 0  <=>  x/2 = pi*k_1 i k_1 należy do I

t_1 = pi*k_1

x/2-t_1 = 0

1/2*x-t_1 = 0 // + t_1

1/2*x = t_1 // : 1/2

x = t_1/1/2

x = 2*t_1

x = 2*pi*k_1 i k_1 należy do I

sin((pi*((3*x)/2))/4) = 0

sin((pi*((3*x)/2))/4) = 0  <=>  (pi*((3*x)/2))/4 = pi*k_2 i k_2 należy do I

t_2 = pi*k_2

(pi*((3*x)/2))/4-t_2 = 0

3/8*pi*x-t_2 = 0 // + t_2

3/8*pi*x = t_2 // : 3/8*pi

x = t_2/(3/8*pi)

x = 8/3*pi^-1*t_2

x = 8/3*pi^-1*pi*k_2 i k_2 należy do I

sin(x/2)*sin((pi*((3*x)/2))/4) = 0  <=>  sin(x/2) = 0 or sin(x/2)*sin((pi*((3*x)/2))/4) = 0  <=>  sin((pi*((3*x)/2))/4) = 0

x in { 2*pi*k_1, 8/3*pi^-1*pi*k_2 }