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Question:
2cos* = 1 cos*=1/2 * = pie/3 how its possible another one cos* = 1/2 * = 2pie/3 how its possible i am not able to understand this in you third vedio of complex number
Answer:

Given, 2 * cos x = 1

=> cos x = 1/2

=> cos x = cos π/3

=> x = π/3

Again, in generel form

x = 2nπ ± π/3, where n ∈ Z

Let x = 2nπ - π/3 , n = 1

=> x = 2π - π/3

=> x = (2*3π - π)/3

=> x =  (6π - π)/3

=> x =  5π/3

So, x = π/3, 5π/3 ∈ [0, 2π]

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