The number of ordered pair (x, y) satisfying the equation `sin^(2) (x+y)+cos^(2) (x-y)=1` which lie on the circle `x^(2)+y^(2)=pi^(2)` is _________.

Answer

12

Explanation

We have `sin^(2) (x+y)= sin^(2) (x-y)`
`:. x+y=n pi pm (x-y)`
`rArr x= (n pi)/2, y in R`
or `y= (n pi)/2, x in R`
Thus, for each of `x=0, pm pi/2`, there are two values of y.
For each of `y=0, pm pi/2`, there are two values of x.
So, total number of orderes pais is 12.