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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: 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.
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