Simplify sin(2x)*cos(x)

Problem

sin(2*x)*cos(x)

Solution

1. Apply the double angle identity for sine, which states sin(2*x)=2*sin(x)*cos(x)

sin(2*x)*cos(x)=(2*sin(x)*cos(x))*cos(x)

2. Multiply the cosine terms together to simplify the expression.

2*sin(x)*cos(x)*cos(x)=2*sin(x)*cos2(x)

3. Use the Pythagorean identity cos2(x)=1−sin2(x) if an alternative form in terms of sine is required.

2*sin(x)*(1−sin2(x))=2*sin(x)−2*sin3(x)

Final Answer

sin(2*x)*cos(x)=2*sin(x)*cos2(x)

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