Question

The equation $\sin x+\sin y+\sin z=-3$for $0\le x\le 2\pi ,0\le y\le 2\pi ,0\le z\le 2\pi ,$ has

Answer 1

The given equation is $\sin x+\sin y+\sin z=–3,0\le x\le 2\pi ,0\le y\le 2\pi ,0\le z\le 2\pi$

We know that $-1\le \sin \theta \le 1$
$$\begin{gathered} \Rightarrow x=y=z={\sin }^{-1}(-1) \\ \Rightarrow x=y=z=\frac{3\pi }{2}forx\le y\le z\le 2\pi \end{gathered}$$

Hence the given equation has one root