Limits Of Trigonometric Functions

Step 1: Understanding the Concept:
Use standard limits: and .

Step 2: Detailed Explanation:


Step 3: Final Answer:
.

Concept:
• as

Step 1: Apply approximation


Step 2: Denominator


Step 3: Compute limit
Final Conclusion:

Concept:
• Use identity:

Step 1: Rewrite expression


Step 2: Use identity


Step 3: Substitute


Step 4: Apply limit
Final Conclusion:

Step 1: Rearrange the given equation.
We are given . We can express this as: Simplifying:
Step 2: Solve for .
Taking the square root of both sides:
Step 3: Compute .
Since we need to find , we have two cases: - If , then: - If , then: Thus, in both cases: