Simplify sin(x/2)-sin(x/3)

Problem

sin(x/2)−sin(x/3)

Solution

1. Identify the appropriate sum-to-product identity for the difference of two sine functions.

sin(A)−sin(B)=2*cos((A+B)/2)*sin((A−B)/2)

2. Assign the values for the variables A and B based on the given expression.

A=x/2

B=x/3

3. Calculate the sum term (A+B)/2 by finding a common denominator.

(x/2+x/3)/2=(3*x+2*x)/6/2

(5*x)/6/2=(5*x)/12

4. Calculate the difference term (A−B)/2 by finding a common denominator.

(x/2−x/3)/2=(3*x−2*x)/6/2

x/6/2=x/12

5. Substitute the calculated terms back into the sum-to-product formula.

2*cos((5*x)/12)*sin(x/12)

Final Answer

sin(x/2)−sin(x/3)=2*cos((5*x)/12)*sin(x/12)

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