Limits Of Trigonometric Functions

Step 1: We are given the expression .
To simplify this, we use the addition formula for inverse tangents:
where and .
Step 2: Substitute the values of and into the formula:

Simplify the numerator:

Now simplify the denominator:

So, the expression becomes:

Step 3: Thus, the value of is .

Right-hand limit (RHL): Approaching , we substitute in the first case:
- Left-hand limit (LHL): Approaching , we substitute in the third case: Using , we get: which is not equal to , thus: