Question

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

• A. $1$
• B. $3$
• C. $5$
• D. $7$

Answer 1

Answer: (B)

$3$

Given, $\sin x\cdot \cos y=1$
$\Rightarrow \sin x=1,\cos y=1$
or $\sin x=-1,\cos y=-1$
if $\sin x=1,\cos y=1$ $\Rightarrow x=\frac{\pi }{2},y=0,2\pi$
if $\sin x=-1,\cos y=-1$ $\Rightarrow x=\frac{3\pi }{2},y=\pi$
Thus possible ordered pairs are
$(\frac{\pi }{2},0),(\frac{\pi }{2},2\pi ),(\frac{3\pi }{2},\pi )$.