Find the general solution for each of the following equations: cos 3x + cos x - cos 2x = 0

Solution:

cos 3x + cos x - cos 2x = 0

2cos {(3x + x) / 2} cos {(3x - x) / 2} - cos 2x= 0 [Because cos A + cos B = 2cos {(A + B) / 2} cos {(A - B) / 2}]

2cos 2x cos x - cos 2x = 0

cos 2x(2cos x - 1) = 0

cos 2x = 0 or 2cos x - 1 = 0

cos 2x = 0 or cos x = 1/2

We know that cos π/2 = 0 and cos π/3 = 1/2.

2x = [(2n + 1)π/2] or cos x = 1/2

x = [(2n + 1)π/4] or x = 2nπ ± π/3, where n ∈ Z.

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 6

Find the general solution for each of the following equations: cos 3x + cos x - cos 2x = 0

Summary:

The general solution of the equation cos 3x + cos x - cos 2x = 0 is x = [(2n + 1)π/4] or x = 2nπ ± π/3, where n∈Z.