Trigonometry system of equations

[jacks]

How can i solve system of equations , if [tex]x,y,z\in \left[0,\frac{\pi}{2}\right)[/tex]


[tex]\begin{cases}\tan x+\sin y+\sin z = 3x\\


\sin x+\tan y+\sin z = 3y\\


\sin x+\sin y+\tan z = 3z\end{cases}[/tex]

 

[soroban]

Hello, jacks!

How can i solve system of equations , if [tex]x,y,z \in \left[0,\tfrac{\pi}{2}\right)[/tex]

[tex]\begin{array}{ccc}\tan x+\sin y+\sin z &=& 3x\\
\sin x+\tan y+\sin z &=& 3y\\
\sin x+\sin y+\tan z &=& 3z\end{array}[/tex]

I don't think you can.
. . The equations are transcendental.

However, by inspection, [tex](x,y,z) \,=\,(0,0,0)[/tex] is a solution.