Final answer:
The expression (cos²x-1)/(sin²xcos²x) simplifies to -sec²x using trigonometric identities.
Step-by-step explanation:
The expression you're asking about, (cos²x-1)/(sin²xcos²x), can be simplified using trigonometric identities. Recall that cos²x + sin²x = 1, which is the Pythagorean identity for sine and cosine. This means that cos²x - 1 is equal to -sin²x.
Substituting -sin²x for cos²x - 1 in the original expression, we get (-sin²x)/(sin²xcos²x). The sin²x terms in the numerator and denominator cancel out, leaving us with -1/cos²x, which is equivalent to -sec²x, since secx is defined as 1/cosx. Hence, the simplified form of the given expression is -sec²x.