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

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Solution

The correct option is B 6
We have, $cos x . sin y = 1$
we know $- 1 \leq cos x, sin y \leq 1$
Hence, $cos x = 1, sin y = 1$ or $cos x = - 1, sin y = - 1$
thus solution in the given interval is,
$x = 0, 2 π, y = \frac{π}{2}, \frac{5 π}{2}$ or $x = π, 3 π, y = \frac{3 π}{2}$
Hence possible number of ordered pair is, $2 \times 2 + 2 \times 1 = 6$
Hence, option 'C' is correct.

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