Find the principal and general solutions of the equation sec x = 2

Question

Find the principal and general solutions of the following equations: sec x = 2

Answer 1

secx=2

⇒ cos x = 1/2

cos x = cos π/3

Using formula for  general soluton of cos x = cos y  i.e x = 2n π  y

We have x = 2n π - π/ 3

The solutions that lie in the interval 0 to 2 π , both included are principal solution

So they are ,  in this case ,

π/3, 2 π- π/ 3 = 5π/ 3