Sin4x - cos4x=sin2x - 1/2

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вопрос

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.