Evaluate the limit of a trigonometric function as x approaches 0 by applying L'Hôpital's rule twice.

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Limit of a Trigonometric Fraction Using L'Hôpital's Rule

Limits core

\(\lim_{x\to 0} \frac{\cos 2x - \cos x}{\sin^2 x}\)

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What you need first

L'Hôpital's rule
Derivatives of trigonometric functions
The chain rule
Double-angle identities

What this problem tests

Tests the ability to recognize indeterminate forms, apply L'Hôpital's rule multiple times, and use trigonometric identities to simplify intermediate steps.

This is a standard Calculus I problem testing the repeated application of L'Hôpital's rule and the simplification of trigonometric expressions.

Limit of a Trigonometric Fraction Using L'Hôpital's Rule

What you need first

What this problem tests

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