The value of `sin^2 47 + cos^2 47` and `sin 42 * csc 42` has to be determined.

Use the fundamental relation `sin^2x + cos^2x = 1`

Here, x = 47, `sin^2 47 + cos^2 47 = 1` .

`csc x = 1/sin x`

`sin 42 * csc 42 = sin 42/sin 42 = 1`

**The value of both `sin^2 47 + cos^2 47` and `sin 42 * csc 42` is 1**