1.

If `x, y in [0,2pi]` then find the total number of order pair `(x,y)` satisfying the equation `sinx .cos y = 1`

Answer» `sinxcosy = 1`
`=> cosy = 1/sinx`
`=> cosy = cosec x`
Now, there are only two cases when `cos theta and cosec theta ` are equal.When both of them are `1` or `-1`.
Case 1: When `cos y = cosecx = 1`
`=>cos y = 1 , cosecx =1`
`=>y = 0,2pi and x = pi/2`
So, ordered pairs in this case are `(pi/2,0) and (pi/2,2pi)`.
Case 2: When `cos y = cosecx = -1`
`=>cos y = -1 , cosecx = -1`
`=>y = pi and x = (3pi)/2`
So, ordered pair in this case is`((3pi)/2,pi)`.
So, there are `3` ordered pairs that satify the given equation.


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