Given; P(n) : cos θ cos 2θ cos22θ ….. cos 2n–1θ = sin 2n θ/2n sin θ
⇒ When n=1 :
It’s true at n = 2.
⇒ When n=3 :cos θ cos 2θ cos 4θ
It’s true at n = 3.
Let n = k
⇒ It’s true at n = k+1.
∴ By Mathematical Induction cos θ cos 2θ cos22θ ….. cos 2n–1θ = sin 2n θ/2n sin θ is true for all natural numbers n.