Final answer:
The expression cos(4α) - 4α does not simplify to a standard trigonometric identity with the given equations. It's possible the question has a typo or is missing context.
Step-by-step explanation:
The question asks to simplify an expression that seems to contain a typo. Assuming the question is intended to ask about simplifying cos(4α) - 4α, it does not simplify to a standard trigonometric identity or a simpler expression using the provided trigonometric equations. However, if the question intended to ask about the double angle formulas like cos(2α), based on these formulas we can derive that:
- cos(2α) = cos^2(α) - sin^2(α)
- cos(2α) = 2cos^2(α) - 1
- cos(2α) = 1 - 2sin^2(α)
None of the provided information immediately leads to a simplification of cos(4α) - 4α, which may indicate the original question was phrased incorrectly or is missing some context.