alleryStart learning →Write cos(6x) in terms of cos(3x) using a double-angle formula.
A2 cos^2(3x) + 1
B2 cos^2(3x) - 1
C1 - 2 cos^2(3x)
D2 cos(3x) - 1
Answer & Solution
Correct answer: B. 2 cos^2(3x) - 1
1. Read 6x as twice 3x, so cos(6x) = cos(2 times 3x).
2. The double-angle formula in cosine alone is cos(2u) = 2 cos^2 u - 1.
3. Setting u = 3x gives cos(6x) = 2 cos^2(3x) - 1.
4. No exact value of x is needed, since the pattern of the identity is what does the work.
5. The option 2 cos(3x) - 1 drops the square and would fail even at x = 0.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.3 Double-Angle, Half-Angle, and Reduction Formulas_
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