Question

If $0\le x\le 2\pi$, $0\le y\le 2\pi$ and $\sin x+\sin y=2$ then the value of $x+y$ is

• A. $\pi$
• B. $\frac{\pi }{2}$
• C. $3\pi$
• D. none of these

Answer 1

The correct option is A $\pi$

We have, $\sin x+\sin y=2$

but we know that maximum value of \sin x is $1$

hence only solution is $\sin x=1$ and $\sin y=1$

so in $0\le x\le 2\pi ,0\le y\le 2\pi$

solution is $x=\frac{\pi }{2},y=\frac{\pi }{2}$

therefore,
$x+y=\pi$

Hence, option 'A' is correct.