Use the product-to-sum identities to rewrite the following expression as a sum or difference.4sin(3x)sin(x)
Question
Use the product-to-sum identities to rewrite the following expression as a sum or difference.4sin(3x)sin(x)
Solution
The product-to-sum identities are given by:
sin(A)sin(B) = 1/2[cos(A-B) - cos(A+B)]
We can use this identity to rewrite the expression 4sin(3x)sin(x) as a sum or difference.
Let A = 3x and B = x. Then the expression becomes:
4sin(A)sin(B) = 4 * 1/2[cos(A-B) - cos(A+B)] = 2[cos(3x-x) - cos(3x+x)] = 2[cos(2x) - cos(4x)]
So, 4sin(3x)sin(x) can be rewritten as 2[cos(2x) - cos(4x)].
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