Evaluating the Limit of tan(x)/sec(x) using Algebraic Manipulation and Trigonometric Identities

Evaluate the limit Lim Tan(x)/Sec(x)x→0

To evaluate the limit, we can use algebraic manipulation and trigonometric identities

To evaluate the limit, we can use algebraic manipulation and trigonometric identities.

First, let’s rewrite the expression as:

lim (tan(x)/sec(x)) as x approaches 0.

Since tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x), we can rewrite the expression as:

lim (sin(x)/cos(x)) / (1/cos(x)).

Now, we can simplify further by multiplying the numerator and denominator by cos(x):

lim (sin(x) * cos(x)) / (cos(x) * 1).

This simplifies to:

lim sin(x).

Finally, we evaluate the limit by plugging in the value of x as it approaches 0:

lim sin(x) = sin(0) = 0.

Therefore, the limit of tan(x)/sec(x) as x approaches 0 is 0.

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