Please explain how to work these problems in steps
1. Prove this identity: sin(x+y)/sin(x-y) = coty+cotx/coty-cotx
8. Simplify: 2sinxcos³x-2sin³xcosx
9. If cosx=-¼and Pi/2 < x < pi, then cos (pi/6 - x) = ?
10. Prove this identity: cos8x=cos²4x-sin²4x
Trigonometric identities are proven and simplifying trigonometric expressions is investigated. The solution is detailed and well presented.