To factor the expression csc²x – 1, we can recognize that this is a difference of squares. The difference of squares can be factored using the formula:
a² – b² = (a – b)(a + b)
In this case, we can let:
a = csc x and b = 1.
Applying the difference of squares formula, we get:
csc²x – 1 = (csc x – 1)(csc x + 1)
Therefore, the factored form of csc²x – 1 is (csc x – 1)(csc x + 1).
This factorization is helpful because it simplifies the expression and can be further analyzed or solved in different contexts of trigonometric equations or identities.