Simplify sin(2x)^2

Problem

sin2(2*x)

Solution

1. Identify the expression as the square of the sine of a double angle, which can be written as (sin(2*x))2

2. Apply the double angle identity for sine, which states sin(2*x)=2*sin(x)*cos(x)

3. Substitute this identity into the squared expression:

(2*sin(x)*cos(x))2

4. Distribute the exponent to each factor inside the parentheses:

2⋅sin2(x)⋅cos2(x)

5. Simplify the numerical coefficient to reach the final form:

4*sin2(x)*cos2(x)

Final Answer

sin2(2*x)=4*sin2(x)*cos2(x)

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