4sin(x/2)cos(x/2)

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Solution for 4sin(x/2)cos(x/2) equation: 


x in (-oo:+oo)

4*sin(x/2)*cos(x/2) = 0

4*sin(x/2) = 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

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

cos(x/2) = 0

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

t_2 = pi*k_2+pi/2

x/2-t_2 = 0

1/2*x-t_2 = 0 // + t_2

1/2*x = t_2 // : 1/2

x = t_2/1/2

x = 2*t_2

x = 2*pi*k_2+pi/2 i k_2 należy do I

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

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

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