Find the general solutions of the following equation: `cos3theta=1/2`

Explanation

Given,`cos 3x = 1/2`

We know that cos x and sec x have positive values in the 1st and 4th quadrant.

∴ `cos 3x = cos π/3`

If cos x = cos y then `x = 2nπ ± y,` where n ∈ Z

Clearly on comparing we have` y = π/3`

∴ `3x = 2nπ ± π/3`

⇒ `x = (2nπ)/3 ± (π)/9` ,where n ϵ Z