Question

If $0\le x\le 3\pi ,0\le y\le 3\pi andcosx.siny=1$ then the possible number of values of the ordered pair $(x,y)$ is

• A. $6$
• B. $12$
• C. $8$
• D. $15$

Answer 1

The correct option is A $6$

$\cos x\sin y=1$
When
1) $\cos x=\sin y=1$
$\Rightarrow x=2n\pi$ and $=\frac{(4n-1)\pi }{2}$
2) $\cos x=\sin y=-1$
$\Rightarrow x=(2n+1)\pi$ and $y=\frac{(4n+3)\pi }{2}$
$\therefore x=0,2\pi y=\frac{\pi }{2},\frac{5\pi }{2}$ or $x=\pi y=\frac{3\pi }{2}$