8 sin 9x cos3x
Rewrite the xpression as a sum or differnce using one of the product sum formulas Simplify if possible
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To rewrite the expression 8 sin 9x cos 3x as a sum or difference, we can use the product-to-sum formula, which states that the product of two trigonometric functions can be written as the sum or difference of two trigonometric functions. The specific formula we will use is:
sin A cos B = (1/2)[sin(A + B) + sin(A - B)]
Using this formula, we can rewrite the expression as:
8 sin 9x cos 3x = (1/2)[sin(9x + 3x) + sin(9x - 3x)]
Simplifying further, we have:
8 sin 9x cos 3x = (1/2)[sin(12x) + sin(6x)]
Therefore, the expression 8 sin 9x cos 3x can be rewritten as (1/2)[sin(12x) + sin(6x)].