Simplify 1+cos(18x)

Problem

1+cos(18*x)

Solution

1. Identify the double angle identity for cosine that relates to 1+cos(θ) The identity is cos(2*θ)=2*cos2(θ)−1

2. Rearrange the identity to isolate the expression of the form 1+cos(2*θ) Adding 1 to both sides gives 1+cos(2*θ)=2*cos2(θ)

3. Substitute 2*θ=18*x into the identity. This implies that θ=9*x

4. Apply the substitution to the expression to find the simplified form.

Final Answer

1+cos(18*x)=2*cos2(9*x)

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