If `x , y in [0,2pi]`
, then find the total number of ordered pairs `(x , y)`
satisfying the equation `sinxcosy=1`
Text Solution
Verified by Experts
`sin x cos y=1` `rArr sin x=1, cos y=1 or sin x=-1, cos y =-1` If `sin x=1. cos y=1`, hence, `x=pi//2, y=0, 2pi` If `sin x=-1, cos y =-1`, hence, `x=3pi//2, y=pi` Thus, the possible ordered ordered pairs are `(pi/2, 0), (pi/2, 2pi)` and `((3pi)/2, pi)`.
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