If ` 0 le x le 3 pi , 0 le y le 3 pi and cos x * sin y=1 `, then find the possible number of values of the orederd pair (x,y) .

Options

A. 6
B. 12
C. 8
D. 15

Answer

A

Explanation

We have,
`"sin"x "cos" y = 1`
`rArr ("sin" x= 1 "and cos" y =1) "or" ("sin" x = -1 "and cos" y = -1)`
Now,
`"sin"x = 1 "and cos" y = 1`
`rArr x = (pi)/(2), (5pi)/(2) "and " y = 0, 2 pi " " [because 0 le x, y le 3 pi]`
`rArr (x, y)` has 4 values.
and, `"sin"x =-1 "and cos" y = -1`
`rArr x = (3pi)/(2) "and" y = pi, 3 pi`
`rArr (x, y)` has 2 values.
Thus, there are 6 ordered pairs.