First of all let's write sin(x-y) = sin(x)cos(y) - cos(x)sin(y) In order lớn have a better writing for the function: g(x, y) = sin(x)(1 + cos(y)) + sin(y)(1 - cos(x)) Now this is a ...

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Find x^2+y^2+z^2 if x+y+z=0 & sinx+siny+sinz=0 và cosx+cosy+cosz=0 for any x,y,z in <-pi,pi>
https://math.stackexchange.com/questions/2083271/find-x2y2z2-if-xyz-0-and-sinx-siny-sinz-0-and-cosx-co
egineqnarray sin z &=& -sin x-sin y\ cos z &=& -cos x-cos y endeqnarray so egineqnarray sin^2z &=& sin^2x+sin^2y+2sin xsin y\ cos^2z &=& cos^2x+cos^2y+2cos xcos y ...
Using Prosthaphaeresis Formulas, sin x+sin y=2sinfracx+y2cosfracx-y2 sin(x+y)=2sinfracx+y2cosfracx+y2 So, sin x+sin y-sin(x+y)=2sinfracx+y2left(cosfracx-y2-cosfracx+y2 ight) ...
Using Lagrange multipliers, & setting up the initial function: Lambda(x, y, z, lambda)=sin(x)+sin(y)+sin(z)+lambda(x+y+z-pi) Setting the gradient ablaLambda=0, we can write: fracpartialLambdapartial x=cos(x)+lambda=0 ...
The standard numerical method for plotting an implicit function graph, say f(x,y) = 0, is lớn evaluate f at points on a triangular grid, see which cells of the grid have a change of sign, & use ...

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Hint : you should start from cos(x) = -cos (x+y), ; cos(y) = -cos(x+y) Rightarrow cos(x) = cos(y). This gives you that x = y + 2pi k or x = 2pi k-y. After that you have lớn solve two ...
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left< eginarray l l 2 & 3 \ 5 & 4 endarray ight> left< eginarray l l l 2 & 0 và 3 \ -1 & 1 & 5 endarray ight>
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