Question

Number of solutions of the equation $sinx+siny+sinz=-3for0\le x\le 2\pi ,0\le y\le 2\pi ,0\le z\le 2\pi$, is

• A. one solution
• B. set of two solution
• C. set of four solution
• D. set of 8 solutions

Answer 1

The correct option is A one solution

As $-1\le \sin \theta \le 1$
$sinx+siny+sinz=-3\Rightarrow \sin x=\sin y=\sin x=-1$
$\Rightarrow x=y=z=\frac{(4n-1)\pi }{2}$
Hence for $0\le x\le 2\pi ,0\le y\le 2\pi ,0\le z\le 2\pi$
Number of solution is $1$