# Trigonometrysystem of equations

#### jacks

##### Well-known member
How can i solve system of equations , if $$x,y,z\in \left[0,\frac{\pi}{2}\right)$$

$$\begin{cases}\tan x+\sin y+\sin z = 3x\\ \sin x+\tan y+\sin z = 3y\\ \sin x+\sin y+\tan z = 3z\end{cases}$$

#### soroban

##### Well-known member
Hello, jacks!

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

$$\begin{array}{ccc}\tan x+\sin y+\sin z &=& 3x\\ \sin x+\tan y+\sin z &=& 3y\\ \sin x+\sin y+\tan z &=& 3z\end{array}$$

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

However, by inspection, $$(x,y,z) \,=\,(0,0,0)$$ is a solution.