Is tan(x + π) = tan x?

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Multiple Choice

Is tan(x + π) = tan x?

Explanation:
Tangent repeats every π, so adding π to the angle doesn’t change its value. Express tan(x+π) as sin(x+π)/cos(x+π). With sin(x+π) = -sin x and cos(x+π) = -cos x, you get tan(x+π) = (-sin x)/(-cos x) = sin x/cos x = tan x, provided cos x ≠ 0. So the equality holds for all x where tan x is defined (i.e., x ≠ π/2 + kπ).

Tangent repeats every π, so adding π to the angle doesn’t change its value. Express tan(x+π) as sin(x+π)/cos(x+π). With sin(x+π) = -sin x and cos(x+π) = -cos x, you get tan(x+π) = (-sin x)/(-cos x) = sin x/cos x = tan x, provided cos x ≠ 0. So the equality holds for all x where tan x is defined (i.e., x ≠ π/2 + kπ).

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