https://file.aiquickdraw.com/mathbot/file/1726235333208yakwmrb6.jpg

The image contains multiple limits and functions, and I can see the following exercises:

### Exercise 8.72: 
1. **(a)** \(\lim_{x \to \frac{\pi}{2}} \frac{\sin^2{x}}{\cos{x}}\)
2. **(b)** \(\lim_{x \to \frac{\pi}{2}} \frac{1 - 2\sin^2{x}}{\sin{x} - \cos{x}}\)
3. **(c)** \(\lim_{x \to 0} \frac{\tan{x}}{\sin{x} - \sin{2x}}\)
4. **(d)** \(\lim_{x \to \frac{\pi}{2}} \frac{\sqrt{\sin{x} + 2} - \sqrt{3}}{\sin{x} + 4 - 2}\)

### Exercise 8.73:
1. **(a)** \(\lim_{x \to 0} \frac{1 - \cos{x}}{\sin{x}}\)
2. **(b)** \(\lim_{x \to 0} \frac{1 + \cos{x}}{\sin{x}}\)

Would you like to focus on any specific question? Let me know if you'd like a solution to any of these limits!

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Here are five related questions you can explore:
1. How do you solve limits that involve trigonometric functions?
2. What are the standard limit results for \(\lim_{x \to 0} \frac{\sin{x}}{x}\) and \(\lim_{x \to 0} \frac{1 - \cos{x}}{x}\)?
3. How does L'Hopital's Rule work in evaluating indeterminate forms of limits?
4. What are common trigonometric identities useful in solving limits?
5. How can limits be used to define derivatives in calculus?

**Tip**: When dealing with indeterminate forms, try simplifying the function first using trigonometric identities or L'Hopital's Rule!

Evaluate the limits presented in exercises 8.72 and 8.73 from the math textbook.

Detailed solutions for evaluating trigonometric limits in exercises 8.72 and 8.73. Learn about key concepts like limits, trigonometric identities, and L'Hopital's Rule. Suitable for high school students in Grades 10-12.

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