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Prove that, cos θ cos 2θ cos22θ ….. cos 2n–1θ = sin 2n θ/2n sin θ for all n ϵ N.

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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.

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