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Domain and Range of Trigonometric Ratios

The domain of...

Question

The domain of the function $f (x) = sec x + tan x$ is

A

R - {(2 n + 1) \frac{π}{2}, n \in Z}

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B

R - {n π, n \in Z}

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C

R - {0}

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D

R

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Solution

The correct option is A $R - {(2 n + 1) \frac{π}{2}, n \in Z}$
Domain of $sec x = R - {(2 n + 1) \frac{π}{2}, n \in Z} = D_{1}$
Domain of $tan x = R - {(2 n + 1) \frac{π}{2}, n \in Z} = D_{2}$
$∴$ Domain of $f (x) = D_{1} \cap D_{2} = R - {(2 n + 1) \frac{π}{2}, n \in Z}$

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Domain and Range of Trigonometric Ratios

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