2cos(2x)/cos(x)

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


D( x )

cos(x) = 0

cos(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

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

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

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

2*cos(2*x) = 0

cos(2*x) = 0

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

t_1 = pi*k_1+pi/2

2*x-t_1 = 0

2*x-t_1 = 0 // + t_1

2*x = t_1 // : 2

x = t_1/2

x = pi*k_1+pi/2/2 i k_1 należy do I

2*cos(2*x) = 0  <=>  2 = 0 or 2*cos(2*x) = 0  <=>  cos(2*x) = 0

x = pi*k_1+pi/2/2

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