The solution of `sin^2x - cos^2x = 3` has to be determined.

`sin^2x - cos^2x = 3`

=> `cos^2x - sin^2x = -3`

=> `cos 2x = -3`

But the range of the cosine function is [-1, 1], `cos 2x = -3` is not true for any value of x.

**The equation `sin^2x - cos^2x = 3` does not have a solution.**