Question

Find the principal solutions of the following equations :

(i) √3 cosec x + 2 = 0

(ii) tan x = - √3

(iii) √3 sec x + 2 = 0 

Answer 1

(i) Given: √3 cosec x + 2 = 0

⇒ cosec x = -2/√3

We know that cosec θ x sin θ = 1

so sin x = -√3/2

Formula used: sinθ = sinα 

⇒ θ = nπ + (-1)ⁿα, n ∈

By using formula, we have

(v) Given: tan x = -√3

Formula used: tanθ = tanα

⇒ θ = nπ ± α, n ∈ l

By using above formula, we have

(iii) Given: √3 sec x + 2 = 0

⇒ sec x = -2/√3

we know that sec θ x cos θ = 1

so cos x = -√3/2