(sin(x)*cos(0.5*x))/x

Solution for (sin(x)*cos(0.5*x))/x equation:

D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(sin(x)*cos(0.5*x))/x = 0

(sin(x)*cos(0.5*x))/x = 0 // * x

sin(x)*cos(0.5*x) = 0

sin(x) = 0

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

t_1 = pi*k_1

x-t_1 = 0

x-t_1 = 0 // + t_1

x = t_1

x = pi*k_1 i k_1 należy do I

cos(0.5*x) = 0

cos(0.5*x) = 0  <=>  0.5*x = pi*k_2+pi/2 i k_2 należy do I

t_2 = pi*k_2+pi/2

0.5*x-t_2 = 0

0.5*x-t_2 = 0 // + t_2

0.5*x = t_2 // : 0.5

x = t_2/0.5

x = 2*t_2

x = 2*pi*k_2+pi/2 i k_2 należy do I

sin(x)*cos(0.5*x) = 0  <=>  sin(x) = 0 or sin(x)*cos(0.5*x) = 0  <=>  cos(0.5*x) = 0

x in { pi*k_1, 2*pi*k_2+pi/2 }