# How do you determine if #secx*tanx# is an even or odd function?

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To determine if ( \sec(x) \tan(x) ) is an even or odd function, we can analyze its behavior under the transformations ( x \to -x ).

For an even function: [ f(-x) = f(x) ]

For an odd function: [ f(-x) = -f(x) ]

Let's evaluate ( \sec(x) \tan(x) ) under the transformation ( x \to -x ):

[ \sec(-x) \tan(-x) ]

Using the even/odd properties of secant and tangent functions: [ \sec(-x) = \sec(x) ] [ \tan(-x) = -\tan(x) ]

Substituting these into ( \sec(-x) \tan(-x) ): [ \sec(-x) \tan(-x) = \sec(x) (-\tan(x)) = -\sec(x) \tan(x) ]

Since ( \sec(-x) \tan(-x) = -\sec(x) \tan(x) ), the function ( \sec(x) \tan(x) ) is an odd function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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