To evaluate the limit of \(\frac{\sin(x)}{\cos^2(x)}\) as \(x\) approaches 1, we proceed as follows:

\[
\lim_{x \to 1} \frac{\sin(x)}{\cos^2(x)}
\]

Since \(\sin(x)\) and \(\cos(x)\) are continuous functions, we can directly substitute \(x = 1\) into the expression:

\[
\sin(1) \approx 0.8415 \quad \text{and} \quad \cos(1) \approx 0.5403
\]

Therefore:

\[
\cos^2(1) = (\cos(1))^2 \approx (0.5403)^2 \approx 0.2919
\]

Now we can compute the limit:

\[
\lim_{x \to 1} \frac{\sin(x)}{\cos^2(x)} \approx \frac{0.8415}{0.2919} \approx 2.882
\]

So,

\[
\lim_{x \to 1} \frac{\sin(x)}{\cos^2(x)} \approx 2.882
\]

Do you want more details or have any questions?

Here are 5 more questions you might want to ask:
1. What is the limit of \(\frac{\sin(x)}{x}\) as \(x\) approaches 0?
2. How do you find the derivative of \(\tan(x)\)?
3. What is the value of \(\lim_{x \to 0} \frac{1 - \cos(x)}{x^2}\)?
4. Can you explain the concept of continuity for trigonometric functions?
5. What is the integral of \(\tan(x)\) with respect to \(x\)?

**Tip:** For limits involving trigonometric functions, remember that direct substitution is often a helpful first step if the functions are continuous at the point of interest.

Learn how to evaluate the limit of sin(x) / cos^2(x) as x approaches 1 with a step-by-step solution. This problem involves using properties of trigonometric functions and limit evaluation techniques. Suitable for advanced high school students or anyone studying calculus.

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