Find the general solution for each of the following equations: sec²2x = 1 - tan 2x

Solution:

sec²2x = 1 - 2tan x

1 + tan²2x = 1 - tan 2x (Using the trigonometric identity, sec²x = 1 + tan²x)

tan²2x + tan 2x = 0

tan 2x(tan 2x + 1) = 0

Now, tan 2x = 0 or tan 2x + 1 = 0 

tan 2x = 0 or tan 2x = -1, where n∈Z.

tan 2x = tan 0 or tan 2x = tan 3π/4, where n∈Z

2x = nπ or 2x = nπ + 3π/4, where n∈Z

x = nπ/2 or x = (nπ/2 + 3π/8), where n∈Z.

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 8

Find the general solution for each of the following equations: sec²2x = 1 - tan 2x

Summary:

The general solutions of the equation sec²2x = 1 - tan 2x are x = nπ/2 or (nπ/2 + 3π/8), where n∈Z.