Evaluate the limit Lim (tan(x)/sin(x))x→0
To evaluate the limit
lim (tan(x) / sin(x)) as x approaches 0,
we can use the concept of limits and apply certain trigonometric identities to simplify the expression
To evaluate the limit
lim (tan(x) / sin(x)) as x approaches 0,
we can use the concept of limits and apply certain trigonometric identities to simplify the expression.
Let’s start by examining the terms involved in the expression.
The tangent function can be defined as the sine of an angle divided by the cosine of that angle. Therefore, we can rewrite the expression as:
lim (sin(x) / cos(x)) / sin(x) as x approaches 0.
Now, we can simplify the expression further by canceling out the sin(x) terms in the numerator and denominator:
lim 1 / cos(x) as x approaches 0.
Now, let’s evaluate the limit as x approaches 0. Since cos(0) = 1, we have:
lim 1 / cos(x) = 1 / cos(0) = 1 / 1 = 1.
Therefore, the limit of (tan(x) / sin(x)) as x approaches 0 is equal to 1.
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