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

Solution:

It is given that cosec x = -2.

We know that cosec is negative in the third and the fourth quadrants.

We know that cosec π/6 = 2.

In the third quadrant, x = π + π/6 = 7π/6 as cosec 7π/6 = cosec (π + π/6) = -cosec π/6 = -2.

In the fourth quadrant, x = 2π - π/6 = 11π/6 as cosec 11π/6 = cosec (2π - π/6) = -cosec π/6 = -2.

Thus, the principle solutions are: x = 7π/6, and 11π/6.

Now,

cosec x = cosec 7π/6

sin x = sin 7π/6

Therefore, x = nπ +(-1)ⁿ 7π/6, where n∈Z is the general solution.

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 4

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

Summary:

The principal solutions are x = 7π/6 and 11π/6 and the general solution is x = nπ +(-1)ⁿ 7π/6, where n∈Z.