1/tan(x/3)/3

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Solution for 1/tan(x/3)/3 equation: 


D( x )

cos(x/3) = 0

tan(x/3) = 0

cos(x/3) = 0

cos(x/3) = 0

cos(x/3) = 0  <=>  x/3 = pi*k_1+pi/2 i k_1 należy do I

t_1 = pi*k_1+pi/2

x/3-t_1 = 0

1/3*x-t_1 = 0 // + t_1

1/3*x = t_1 // : 1/3

x = t_1/1/3

x = 3*t_1

x = 3*pi*k_1+pi/2 i k_1 należy do I

tan(x/3) = 0

tan(x/3) = 0

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

t_2 = pi*k_2

x/3-t_2 = 0

1/3*x-t_2 = 0 // + t_2

1/3*x = t_2 // : 1/3

x = t_2/1/3

x = 3*t_2

x = 3*pi*k_2 i k_2 należy do I

x in {( -oo : +oo ) / {< 3*pi*k_1+pi/2 : 3*pi*k_1+pi/2 > U < 3*pi*k_2 : 3*pi*k_2 >}} i k_2 -> {I}, k_1 -> {I}

(1/tan(x/3))/3 = 0

(1/tan(x/3))/3 = 0 // * 3

1/tan(x/3) = 0

1/tan(x/3) = 0 // * tan(x/3)

1 = 0

x belongs to the empty set

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