Simplify 2sin(2x)^2

Problem

2*sin(2*x)

Solution

1. Identify the expression as a trigonometric term involving the square of a sine function, which can be written as 2*(sin(2*x))2

2. Apply the power-reduction formula for sine, which states sin(θ)=(1−cos(2*θ))/2

3. Substitute θ=2*x into the power-reduction formula.

2*sin(2*x)=2*((1−cos(2*(2*x)))/2)

4. Simplify the expression by canceling the constant factor of 2 and multiplying the arguments inside the cosine function.

2*sin(2*x)=1−cos(4*x)

Final Answer

2*sin(2*x)=1−cos(4*x)

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