Simplify 1-cos(12x)

Problem

1−cos(12*x)

Solution

1. Identify the relevant trigonometric identity for expressions of the form 1−cos(θ)

2. Apply the half-angle identity for sine, which states 1−cos(θ)=2*sin2(θ/2)

3. Substitute θ=12*x into the identity.

4. Simplify the argument of the sine function by calculating (12*x)/2=6*x

Final Answer

1−cos(12*x)=2*sin2(6*x)

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