Please see the attachment for the exact notations and questions in their original format. Basically, what I need help with is the following:
1) Use formulas for lower powers to rewrite the expression in terms of the first power of cosine.
a) cos (^4)x
b) (cos (^4)x) (sin (^2)x)
c) cos (^6)x
2) Prove the identity
a) 4 [(sin (^6)x) + (cos (^6)x)] = 4-3(sin (^2)2x)
b) Show that cos100 - cos200 = sin50
c) Show that cos87-cos33 = sin63
d) cot(x+y) = ((cotx)(coty) - 1)/cotx + coty
e) cos (x+y) cos (x-y) = cos (^2)x - sin (^2)y
f) tan (x-y) + (tany-z) + tan (z-x) = tan (x-y) (tany-z) (tanz-x)
Trigonometry problems and identities are examined.