de Moivre's (1 Viewer)

[asharnadeem]

(a)Use de Moivre’s theorem to express sin 8θ /sin θ cos θ as a polynomial in s, where s = sin θ.
(b) Hence solve the equation x ^6 − 6x ^4 + 10x ^2 − 4 = 0, leaving the roots in trigonometric form

 

[beetree1]

a) let z = cis θ
z^8 = (cis θ)^8 = cos 8θ +isin8θ (De Moivre's) = (cosθ +isinθ)^8 and expand this and then equate imaginary parts.

b) change all the 'cosθ' from part a into sinθs and let sinθ = x and let sin8θ =1 then you can solve using trig

hope this made sense