Simplify sin(8x)cos(8x)

Problem

sin(8*x)*cos(8*x)

Solution

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

2. Rearrange the identity to solve for the product of sine and cosine: sin(θ)*cos(θ)=1/2*sin(2*θ)

3. Substitute θ=8*x into the rearranged identity.

4. Simplify the argument of the sine function by calculating 2⋅8*x=16*x

Final Answer

sin(8*x)*cos(8*x)=1/2*sin(16*x)

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