Simplify 1-sin(2x)^2

Problem

1−sin2(2*x)

Solution

1. Identify the trigonometric identity that relates 1 and the square of a sine function.

2. Apply the Pythagorean identity, which states sin2(θ)+cos2(θ)=1

3. Rearrange the identity to solve for the cosine term: cos2(θ)=1−sin2(θ)

4. Substitute the argument 2*x for θ in the identity.

5. Simplify the expression by replacing 1−sin2(2*x) with its equivalent cosine form.

Final Answer

1−sin2(2*x)=cos2(2*x)

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