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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