sin^2x (Power to Double Angle)
1/2(1-cos2x)
Applying the power to double angle formula to sin^2x, we get:
sin^2(2x) = (2sinx cosx)^2
sin^2(2x) = 4sin^2x cos^2x
Using the trigonometric identity sin^2x + cos^2x = 1, we can express cos^2x as 1 – sin^2x. Thus, substituting this into the equation above, we get:
sin^2(2x) = 4sin^2x(1 – sin^2x)
Expanding the equation, we get:
sin^2(2x) = 4sin^2x – 4sin^4x
Therefore, sin^2(2x) can be expressed in terms of sin^2x as:
sin^2(2x) = 2(2sin^2x – 2sin^4x)
This is the double angle formula for sin^2x.
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