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.
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.