Simplify cos(2t)

Problem

cos(2*t)

Solution

1. Identify the expression as a double angle trigonometric function.

2. Apply the double angle formula for cosine, which has three common equivalent forms.

3. Select the primary form based on the identity cos(2*θ)=cos^2(θ)−sin^2(θ)

4. Alternative forms can be derived using the Pythagorean identity sin^2(t)+cos^2(t)=1 resulting in 2*cos^2(t)−1 or 1−2*sin^2(t)

Final Answer

cos(2*t)=cos^2(t)−sin^2(t)

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