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I am trying to solve this system of equations but without any results.

How can I solve this system of equations (in real numbers)?

$\sin^2 x + \cos^2 y = \tan^2 z$

$\sin^2 y + \cos^2 z = \tan^2 x$

$\sin^2 z + \cos^2 x = \tan^2 y$

Thanks in advance.

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    The inherent symmetry in these equations suggests trying whether there are solutions of the form $x=y=z$. Of course, there might be other solutions as well.2012-12-02

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Try converting each term to sine: $\sin^2x + (1-\sin^2y) = {\sin^2z \over 1-\sin^2z}$ $\sin^2y + (1-\sin^2z) = {\sin^2x \over 1-\sin^2x}$ $\sin^2z + (1-\sin^2x) = {\sin^2y \over 1-\sin^2y}$ If you substitute A, B, and C for $\sin^2x, \sin^2y, \sin^2z$, you'll have three equations with three unknowns, so you should be able to solve from there.

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    Note that if you just write out function names like $\sin$, they get interpreted as juxtaposed variable names and formatted (e.g. italicized) accordingly. To get the proper font and spacing for such functions, you can use the predefined commands like `\sin`, or if you need a function for which there's no predefined command, you can use `\operatorname{name}`.2012-12-02