Question

If $x,y\in [0,2\pi ]$, then total number of ordered pairs $(x,y)$ satisfying the equation $\sin x.\cos y=1$ is equal to

• A. $1$
• B. $3$
• C. $5$
• D. $7$

Answer 1

The correct option is B $3$

$\sin x.\cos y=1$
$\Rightarrow \sin x=1,\cos y=1$ or $\sin x=-1,\cos y=-1$
Hence, the ordered pairs of $(x,y)$ are $(\frac{\pi }{2},0)$ , $(\frac{\pi }{2},2\pi )$ ,$(\frac{3\pi }{2},\pi )$