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If x in (0,2pi)a n dy in (0,2pi) , then ...

If `x in (0,2pi)a n dy in (0,2pi)` , then find the number of distinct ordered pairs `(x , y)` satisfying the equation `9cos^2x+sec^2y-6cosx-4secy+5=0`

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`9 cos^(2) x+sec^(2) y-6 cos x-4 sec y+5=0`
`rArr (3 cos x-1)^(2)+(sec y-2)^(2)=0`
`rArr cos x =1/3` and `sec y=2` (simultaneously)
`:.` Number of distance x in `(0, 2pi)` is 2 and number of distinct y in `(0, 2pi)` is 2.
`:.` Number of distinct ordered pairs `(x, y)=2xx2=4`
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