Simplify 6sin(x)cos(x)

Problem

6*sin(x)*cos(x)

Solution

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

2. Rewrite the original expression to isolate the factor of 2 required for the identity.

6*sin(x)*cos(x)=3*(2*sin(x)*cos(x))

3. Substitute the identity sin(2*x) into the expression.

3*(2*sin(x)*cos(x))=3*sin(2*x)

Final Answer

6*sin(x)*cos(x)=3*sin(2*x)

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