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Use the product to sum formula to fill in the blanks in the identity below:

sin(9x) cos(8x)=1/2 (sin blank x + sin blank x)

User Spkersten
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To fill in the blanks using the product to sum formula, we can express the right side of the equation as a sum of two sine functions. The product to sum formula states that:

sin(A)cos(B) = 1/2 [sin(A + B) + sin(A - B)]

In this case, we have sin(9x)cos(8x) on the left side, so we can rewrite it using the formula:

sin(9x)cos(8x) = 1/2 [sin(9x + 8x) + sin(9x - 8x)]

Simplifying the expressions inside the brackets, we get:

sin(9x + 8x) = sin(17x)

sin(9x - 8x) = sin(x)

Therefore, the filled identity becomes:

sin(9x)cos(8x) = 1/2 [sin(17x) + sin(x)]

So, the blanks are filled as sin(17x) and sin(x).

User Only Bolivian Here
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