Simplify sin(x/2)cos(x/2)

Problem

sin(x/2)*cos(x/2)

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 by dividing both sides by 2 resulting in sin(θ)*cos(θ)=1/2*sin(2*θ)

3. Substitute θ=x/2 into the rearranged identity.

4. Simplify the argument of the sine function by calculating 2⋅x/2=x

Final Answer

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

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