To simplify the given equation, we will use the double angle formula for sine, which states that sin(2θ) = 2sin(θ)cos(θ).
Given equation: sin(4x) - cos(4x) = sin(2x) - 1/2
We know that sin(4x) = 2sin(2x)cos(2x) and cos(4x) = 2cos^2(2x) - 1
Substitute these values into the given equation:2sin(2x)cos(2x) - 2cos^2(2x) + 1 = sin(2x) - 1/2
Now, we want to simplify:2sin(2x)cos(2x) - 2cos^2(2x) + 1 = 2sin(2x)cos(2x) - 2cos^2(2x) + 1
Therefore, the equation is proven to be true.
To simplify the given equation, we will use the double angle formula for sine, which states that sin(2θ) = 2sin(θ)cos(θ).
Given equation: sin(4x) - cos(4x) = sin(2x) - 1/2
We know that sin(4x) = 2sin(2x)cos(2x) and cos(4x) = 2cos^2(2x) - 1
Substitute these values into the given equation:
2sin(2x)cos(2x) - 2cos^2(2x) + 1 = sin(2x) - 1/2
Now, we want to simplify:
2sin(2x)cos(2x) - 2cos^2(2x) + 1 = 2sin(2x)cos(2x) - 2cos^2(2x) + 1
Therefore, the equation is proven to be true.