The number of ordered pairs (x,y) satisfying `x(sin^(2)x+(1)/x^(2))=2sinx sin^(2)y` where `x in (-pi,0)uu(0,pi)` and `yin[0,2pi]` is.

Answer

8

Explanation

`x(sin^(2)x+(1)/(x^(2)))=2sinxsin^(2)y`
`impliessin^(2)x+(1)/(x^(2))=2((sinx)/(x))sin^(2)y`
`impliessin x = (1)/(x)" and" sin ^(2)y =1 {because sin^(2)x+(1)/(x^(2))ge2.(sinx)/(x)}`