Verify the Identity sin(6x)=2sin(3x)cos(3x)

Problem

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

Solution

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

2. Substitute the value θ=3*x into the double angle formula.

3. Observe that 2*θ=2*(3*x)=6*x

4. Rewrite the left side of the identity using the substitution to show it matches the right side.

Final Answer

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

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