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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
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.
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