Mastering The Double Angle Formula For Sin^2X: A Comprehensive Guide

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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