tan(pi/x)

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Solution for tan(pi/x) equation: 


D( x )

x = 0

cos(pi/x) = 0

x = 0

x = 0

cos(pi/x) = 0

cos(pi/x) = 0

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

t_1 = pi*k_1+pi/2

pi/x-t_1 = 0

pi*x^-1 = t_1 // : pi

x^-1 = t_1/pi

-1 < 0

1/(x^1) = t_1/pi // * x^1

1 = (t_1/pi)*x^1 // : t_1/pi

1/(t_1/pi) = x^1

x = 1/(t_1/pi)

x = 1/(pi*k_1+pi/2/pi) i k_1 należy do I

x in {( -oo : +oo ) / {< 0 : 0 > U < 1/(pi*k_1+pi/2/pi) : 1/(pi*k_1+pi/2/pi) >}} i k_1 -> {I}

tan(pi/x) = 0

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

t_1 = pi*k_1

pi/x-t_1 = 0

pi*x^-1 = t_1 // : pi

x^-1 = t_1/pi

-1 < 0

1/(x^1) = t_1/pi // * x^1

1 = (t_1/pi)*x^1 // : t_1/pi

1/(t_1/pi) = x^1

x = 1/(t_1/pi)

x = 1/(pi*k_1/pi) i k_1 należy do I

x = 1/(pi*k_1/pi)

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