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

Solution:

It is given that sec x = 2

We know that sec is positive in the first and the fourth quadrants.

In the first quadrant, x = π/3 as sec π/3 = 2.

In the fourth quadrant, x = 2π - π/3 = 5π/3 as sec 5π/3 = sec (2π - π/3) = sec π/3 = 2.

Thus, the principle solutions are: x = π/3, and 5π/3.

Now,

sec x = sec π/3

cos x = cos π/3

Therefore, x = 2nπ ± π/3, where n∈Z is the general solution.

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 2

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

Summary:

The principal solutions are x = π/3 and 5π/3 and the general solution is x = 2nπ ± π/3, where n∈Z.