Simplify 2cos(5x)^2-1

Problem

2*cos(5*x)−1

Solution

1. Identify the structure of the expression as a variation of a known trigonometric identity.

2. Recall the double-angle identity for the cosine function, which states cos(2*θ)=2*cos(θ)−1

3. Substitute the value θ=5*x into the identity.

4. Multiply the terms inside the cosine function to find the simplified form.

2*cos(5*x)−1=cos(2⋅5*x)

cos(2⋅5*x)=cos(10*x)

Final Answer

2*cos(5*x)−1=cos(10*x)

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