If $0 \leq x \leq 3 π, 0 \leq y \leq 3 π$ and $cos x . sin y = 1$ , then the possible number of ordered pair $(x, y)$ is:

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Solution

The correct option is C 6
$c o s x . s i n y = 1$
we know $- 1 \leq c o s x, s i n y \leq 1$
Hence, $c o s x = 1, s i n y = 1$ or $c o s x = - 1, s i n y = - 1$
thus solution in the given interval is,
$x = 0, 2 π, y = \frac{π}{2}, \frac{5 π}{2}$ or $x = π, 3 π, y = \frac{3 π}{2}$
Thus possible number of ordered pair is, $2 \times 2 + 2 \times 1 = 6$
Hence, option 'C' is correct.

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