Simplify 3sin(4x)

Problem

3*sin(4*x)

Solution

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

2. Rewrite the argument 4*x as 2*(2*x) to prepare for the application of the identity.

3. Apply the formula by substituting θ=2*x into the identity, resulting in sin(4*x)=2*sin(2*x)*cos(2*x)

4. Substitute this expression back into the original term, multiplying by the coefficient 3

5. Simplify the expression by multiplying the constants 3 and 2

Final Answer

3*sin(4*x)=6*sin(2*x)*cos(2*x)

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