Simplify sin(2x)-cos(2x)

Problem

sin(2*x)−cos(2*x)

Solution

1. Identify the double angle identities for sine and cosine.

2. Apply the identity for sine, which is sin(2*x)=2*sin(x)*cos(x)

3. Apply the identity for cosine, which is cos(2*x)=cos2(x)−sin2(x)

4. Substitute these identities into the original expression.

5. Distribute the negative sign through the cosine identity terms.

Final Answer

sin(2*x)−cos(2*x)=2*sin(x)*cos(x)−cos2(x)+sin2(x)

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