Answer: sin(2x)
In other words, you'll type "sin" without quotes in the green box.
Also, you'll type "2" in the gray box, which also won't have quotes.
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Explanation:
We'll use the first hint. Note the pattern of sin cos +- cos sin which matches (somewhat) with the original expression.
Specifically, we'll use this identity
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
In this case, A = 3x and B = x
So,
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
sin(A)cos(B) - cos(A)sin(B) = sin(A - B)
sin(3x)cos(x) - cos(3x)sin(x) = sin(3x - x)
sin(3x)cos(x) - cos(3x)sin(x) = sin(2x)
