Simplify sin(6x)sin(4x)

Problem

sin(6*x)*sin(4*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=4*x into the formula.

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

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

sin(6*x)*sin(4*x)=1/2*(cos(2*x)−cos(10*x))

Final Answer

sin(6*x)*sin(4*x)=1/2*(cos(2*x)−cos(10*x))

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