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. $Noneofthese$

Answer 1

The correct option is A $\pi$

Given:

$x,y\in [0,2\pi ]$

$\sin x+\sin y=2$

We know that,

$-1\le \sin x\le 1$

$-1\le \sin y\le 1$

Add both the above expressions.

$-2\le \sin x+\sin y\le 2$

Therefore, if

$\sin x+\sin y=2$

$\Rightarrow \sin x=1$

$\Rightarrow \sin y=1$

Therefore,

$\Rightarrow x=\frac{\pi }{2}$ and $\Rightarrow y=\frac{\pi }{2}$

Therefore,

$x+y=\frac{\pi }{2}+\frac{\pi }{2}=\pi$

Hence, this is the required result.