Trigonometric EquationHard

Question

Find the general solution of x, 1 + cosx + cos2x = 0

Options

A.(2n - 1) ; n ∈ I
B.(2n + 1) ; n ∈ I
C.(2n + 1) ; n ∈ I
D.(2n + 1) ; n ∈ I

Solution

1 + cos x + cos 2x = 0
2 cos2x + cos x = 0
⇒ cos x[2 cos x + 1] = 0
cos x = 0 ⇒ x = (2n + 1) , (2n - 1)

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