(a) Use the formula e2i (ei)2 to deduce the well known trigonometric identities for cos 2 and sin 2 (b) Derive the corresponding identities for cos 3 and sin 3 (c) Write down the explicit identities for cos m and sin as polynomials in cos and sin Hint Apply the Binomial Formula to (ei)m ...

a e 2 i cos2 i sin 2 while e i 2 cos i sin ...

(a) Use the formula e2i = (ei)2 to deduce the well-known trigonometric identities for cos 2 and...

Question:

(a) Use the formula e2iθ = (eiθ)2 to deduce the well-known trigonometric identities for cos 2θ and sin 2θ.
(b) Derive the corresponding identities for cos 3θ and sin 3θ.
(c) Write down the explicit identities for cos mθ and sinθ as polynomials in cosθ and sinθ. Hint: Apply the Binomial Formula to (eiθ)m.