Question

If cot θ + tan θ = 2 cosec θ, then find the general value of θ.

Answer 1

According to the question,

⇒ 1 = 2 cosec θ sin θ cos θ

We know that,

sin θ cosec θ = 1

⇒ 1 = 2 cos θ

⇒ cos θ = 1/2 = cos(π/3)

Hence,

The solution of cos x = cos α can be given by,

x = 2mπ ± α ∀ m ∈ Z

⇒ θ = 2nπ ± π/3, n ∈ Z