Answer
$\sin{7x}$
Work Step by Step
$\sin{(A-B)} = \sin{A} \cos{B} - \cos{A} \sin{B}$
$\therefore \sin{8x} \cos{x} -\cos{8x} \sin{x} = \sin{(8x-x)} = \sin{7x}$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.