Find the general solution for each of the following equations: cos 4x = cos 2x

Solution:

cos 4x - cos 2x = 0

-2sin {(4x + 2x) / 2} sin {(4x - 2x) / 2} = 0 [Because cos A - cos B = -2sin {(A + B) / 2} sin {(A - B) / 2}]

sin 3x sin x = 0

sin 3x = 0 or sin x = 0

3x = nΠ  + 0 or x = nΠ + 0  where n∈Z.

x = nΠ/3 or x = nΠ

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 5

Find the general solution for each of the following equations: cos 4x = cos 2x

Summary:

The general solutions of the equation cos 4x = cos 2x are x = nΠ/3 or nΠ, where n∈Z.