Simplify cos(12x)

Problem

cos(12*x)

Solution

1. Identify the expression as a trigonometric function with a multiple angle, specifically cos(n*x) where n=12

2. Apply the double angle formula for cosine, which states cos(2*θ)=2*cos2(θ)−1 or cos(2*θ)=1−2*sin2(θ)

3. Rewrite the expression by treating 12*x as 2*(6*x)

cos(12*x)=2*cos2(6*x)−1

4. Recognize that "Simplify" for a single trigonometric term often implies expressing it in terms of smaller angles or noting that it is already in its simplest functional form. Without further context (such as an identity to prove or an equation to solve), the expression cos(12*x) is already considered simplified.

Final Answer

cos(12*x)=cos(12*x)

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