Simplify sin(6x)sin(2x)

Problem

sin(6*x)*sin(2*x)

Solution

1. Identify the product-to-sum formula for the product of two sine functions.

sin(A)*sin(B)=1/2*(cos(A−B)−cos(A+B))

2. Substitute the values A=6*x and B=2*x into the formula.

sin(6*x)*sin(2*x)=1/2*(cos(6*x−2*x)−cos(6*x+2*x))

3. Simplify the arguments inside the cosine functions by performing the subtraction and addition.

sin(6*x)*sin(2*x)=1/2*(cos(4*x)−cos(8*x))

4. Distribute the constant factor to express the result as a difference of terms.

sin(6*x)*sin(2*x)=1/2*cos(4*x)−1/2*cos(8*x)

Final Answer

sin(6*x)*sin(2*x)=1/2*cos(4*x)−1/2*cos(8*x)

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