Question

Find the general solution of the following equation:

(i) sin 2x = 1/2

(ii) cos 3x = 1/√2

(iii) tan 2x/3 = √3

Answer 1

To Find: General solution.

(i) Given: sin 2x = 1/2

Formula used: sin θ = sin α

⇒ θ = nπ + (-1)n α, n ∈ l

By using above formula, we have

So general solution is x = nπ/2 + (-1)ⁿ. π/12 where n ∈ l

(ii) Given: cos 3x = 1/√2

Formula used: cos θ = cos α

⇒ θ = 2nπ ± α, n ∈ l

By using above formula, we have

So general solution is x = 2nπ/3 ± π/12 where n ∈ l

(iii) Given: tan 2x/3 = √3

Formula used: tan θ = tan α

⇒ θ = nπ + α, n ∈ l

By using above formula, we have

So general solution is x = (3n + 1)π/2, where n ∈ l