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

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

D( x )

cos(4*x) = 0

cos(4*x) = 0

cos(4*x) = 0

cos(4*x) = 0  <=>  4*x = pi*k_1+pi/2 i k_1 należy do I

t_1 = pi*k_1+pi/2

4*x-t_1 = 0

4*x-t_1 = 0 // + t_1

4*x = t_1 // : 4

x = t_1/4

x = pi*k_1+pi/2/4 i k_1 należy do I

x in {( -oo : +oo ) / < pi*k_1+pi/2/4 : pi*k_1+pi/2/4 >} i k_1 -> {I}

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

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

cos(x)*sin(x) = 0

cos(x) = 0

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

t_1 = pi*k_1+pi/2

x-t_1 = 0

x-t_1 = 0 // + t_1

x = t_1

x = pi*k_1+pi/2 i k_1 należy do I

sin(x) = 0

sin(x) = 0  <=>  x = pi*k_2 i k_2 należy do I

t_2 = pi*k_2

x-t_2 = 0

x-t_2 = 0 // + t_2

x = t_2

x = pi*k_2 i k_2 należy do I

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

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