Determining sin^2(2x) using the double angle identity for sine

sin^2x (Power to Double Angle)

To determine sin^2(2x), we can use the double angle identity for sine, which states that sin(2x) = 2sin(x)cos(x)

To determine sin^2(2x), we can use the double angle identity for sine, which states that sin(2x) = 2sin(x)cos(x).

Let’s start by squaring sin(2x):

(sin(2x))^2 = (2sin(x)cos(x))^2

Using the property of squaring a product, this can be rewritten as:

(2^2)(sin(x)^2)(cos(x)^2)

Simplifying further:

4sin^2(x)cos^2(x)

So, sin^2(2x) is equal to 4sin^2(x)cos^2(x).

It is important to note that this expression represents the square of the sine of twice an angle, not the sine squared.

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