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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=12473489459765365053)
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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=5291422600673429069)
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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=7344800328378764895)
So general solution is x = (3n + 1)π/2, where n ∈ l