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

Solution:

It is given that cot x = -√3

We know that cot is negative in the second and the fourth quadrants.

We know that cot π/6 = √3.

In the second quadrant, x = π - π/6 = 5π/6 as cot 5π/6 = cot (π - π/6) = -cot π/6 = -√3

In the fourth quadrant, x = 2π - π/6 = 11π/6 as cot 11π/6 = cot (2π - π/6) = -cot π/6  = -√3

Thus, the principle solutions are: x = 5π/6, and 11π/6.

Now,

cot x = cot 5π/6

tan x = tan 5π/6

Therefore, x = nπ + 5π/6, where n∈Z is the general solution.

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 3

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

Summary:

The principal solutions are x = 5π/6 and 11π/6 and the general solution is x = nπ + 5π/6, where n∈Z.