Question

Solve for x,in the equation cos3x+cosx=2cosx,where0

Answer 1

Answer:

Explanation:

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

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

2 cos [(3x + x)/2] .cos [(3x-x)/2] - cos 2x = 0 

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

cos 2x  [ 2 cos  x  - 1 ]                             = 0 

cos 2x  = 0  or cos x = 1/2                       = cos π/3

2x = (2n +1 )π/2 or x = 2mπ +- π/3

x = (2n + 1 ) π/4 or x = 2mπ +- π/3 ; where  n , m ∈ I

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