The expression 4 - cos² A is equivalent to

1)5 - sec² A
2)5 - sin² A
3)5 + sin² A
4)5/sec² A

4 - (1-sin^2 A)

so suspect another typo

4 + cos^2 A
4 + (1-sin^2 A)
5 - sin^2 A

To determine which expression is equivalent to 4 - cos² A, we can use the Pythagorean identity: sin² A + cos² A = 1.

Starting with the given expression, 4 - cos² A, we can rewrite it using the Pythagorean identity:

4 - cos² A = (1 - sin² A) - cos² A
= 1 - sin² A - cos² A

From the Pythagorean identity, we know that sin² A + cos² A is equal to 1. Therefore, we can substitute sin² A + cos² A in place of 1:

1 - sin² A - cos² A = 1 - (sin² A + cos² A)
= 1 - 1
= 0

As a result, the given expression is equivalent to 0. Thus, none of the provided options (1) 5 - sec² A, (2) 5 - sin² A, (3) 5 + sin² A, and (4) 5/sec² A) correctly represent the given expression.