Q17 of 76 Page 52

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

Correct question: cot θ + tan θ = 2cosecθ

Given,


⇒


⇒ {∵ sin2θ + cos2θ = 1}


⇒ 1 = 2 cosec θ sin θ cos θ


⇒ 1 = 2 cos θ {∵ sin θ cosec θ = 1}


⇒ cos θ = 1/2 = cos(π/3)


∵ solution of cos x = cos α is given by


x = 2mπ ± α ∀ m ∈ Z


⇒ θ = 2nπ ± π/3, n ∈ Z


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