Find the principal and general solutions of the following equations: tan x = √3

Solution:

It is given that tan x = √3, which is positive.

We know that tan is positive in the first and the third quadrants.

In the first quadrant, x = π/3 as tan π/3 = √3

In the third quadrant, x = π + π/3 = 4π/3 as  tan 4π/3 = tan (π + π/3) = tan π/3 = √3

Thus, the principle solutions are: x = π/3, and 4π/3

Now,

tan x = tan π/3

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

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 1

Find the principal and general solutions of the following equations: tan x = √3

Summary:

The principal solutions of the equation tan x = √3 are x = π/3 and 4π/3 and the general solution is x = nπ + π/3, where n∈Z.