Final answer:
The trigonometric expression is simplified using the sine difference identity, resulting in sin(-x/6), which is option c.
Step-by-step explanation:
The student's question pertains to simplifying a trigonometric expression that resembles the sine addition and subtraction formulas. To simplify the expression sin(7x/3)cos(5x/2) - cos(7x/3)sin(5x/2), we recognize this as the sine of a difference based on the identity noted in the reference:
sin (a ± β) = sin a cos β ± cos a sin β
Applying this identity to our expression, we get:
sin((7x/3) - (5x/2))
Now, we need to find a common denominator to combine the fractions:
sin((14x/6) - (15x/6)) = sin(-x/6)
Thus, the simplified form of the given expression is sin(-x/6), which corresponds to option c.