sin^4 x (cos^2 x)=(1/16)(1-cos 2x)(1-cos4x)
work one 1 side only!
To simplify the given equation on one side, we can start by expanding the terms on both sides of the equation and then simplifying each side separately.
Let's begin by expanding the left side of the equation:
sin^4(x) * cos^2(x) = (sin^2(x))^2 * (cos^2(x)) = (sin^2(x) * cos^2(x))^2
Next, let's expand the right side of the equation:
(1/16)(1 - cos(2x))(1 - cos(4x))
First, let's expand the parentheses by using the distributive property:
(1/16)(1 - cos(2x) - cos(4x) + cos(2x) * cos(4x))
We can simplify the expression further by combining like terms:
(1/16)(1 - cos(4x) - cos(2x) + cos(2x) * cos(4x))
Now, to simplify the equation, let's focus on the right side only:
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