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Question

Find the general solution for the following equation: 

cos 3x+ cos x - cos 2x = 0
 


Solution

cos 3x + cos x - cos 2x = 0 

2 cos (3x+x2)cos(3xx2) - cos 2x = 0

2 cos 2x cos x - cos 2x =0 

cos 2x (2 cos x-1) = 0 

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

2x = (2n+1) π2

or cos x = 12 = cos π3, n ϵ Z

x = (2n+1) π4

or x = 2nπ±π3, n ϵ Z.


Mathematics

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