tan(x/2)sin(x)=0

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Solution for tan(x/2)sin(x)=0 equation:


D( x )

cos(x/2) = 0

cos(x/2) = 0

cos(x/2) = 0

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

t_1 = pi*k_1+pi/2

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+pi/2 i k_1 należy do I

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

tan(x/2)*sin(x) = 0

tan(x/2) = 0

tan(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

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

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

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

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