cos θ = 1

How to find the general solution of an equation of the form cos θ = 1?

Prove that the general solution of cos θ = 1 is given by θ = 2nπ, n ∈ Z.

Solution:

We have,

cos θ = 1

⇒ cos θ = cos 0°

⇒ θ = 2nπ ± 0°, n ∈ Z, [Since, the general solution of cos θ = cos ∝ is given by θ = 2nπ ± ∝, n ∈ Z.]

⇒ θ = 2nπ, n ∈ Z

Hence, the general solution of cos θ = 1 is θ = 2nπ, n ∈ Z.

Trigonometric Equations

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