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AP ICET 2024 6th May 2024 Shift 1

Question : 181 of 200

Marks: +1, -0

\tan\left(\;\frac{-23}{3}\pi\right) =

Solution:

We know that tan(θ + nπ) = tan(θ), where n is an integer. First, simplify the argument of the tangent:

-\;\frac{23}{3}\pi = -8\pi - \;\frac{\pi}{3}

Since

\tan(\theta+\pi) = -\tan(\theta)

, this becomes:

\tan\left(-8\pi - \;\frac{\pi}{3}\right) = \tan\left(\;\frac{\pi}{3}\right) = \sqrt{3}

Quick Tip

For tangent functions with angles involving multiples of π, use the periodicity of

the tangent function to simplify the argument.

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