Question

If cot θ = sin 2θ, where θ ≠ nπ, n is integer then θ equals to
1. 45^∘ and 60∘ 
2. 45∘ and 90∘ 
3. 45∘ only
4. 90^∘ only
5.

Answer 1

Correct Answer - Option 2 : 45∘ and 90∘ 

Formula used:

sin 2θ = 2sin θ.cos θ

\(\frac{cos\ θ}{sin\ θ}\ = \ cot\ \theta\)

Calculation:

Given that,

cot θ = sin 2θ,

where θ ≠ nπ, n is an integer 

⇒ \(\frac{cos\ θ}{sin\ θ}\ =\ 2sin\ θ.cos\ θ\)

⇒ cos θ.(2sin²θ - 1) = 0

Case:1 cos θ = 0

⇒ θ = 90^∘ 

Case:2 (2sin2θ - 1) = 0

⇒ sin θ = 1/√2

⇒ θ = 45^∘