If : `A+B = 90^(@),and tanA=3/4 "then" : cot B =`

Options

A. -1
B. 0
C. 3/4
D. `sqrt2`

Answer

To solve the problem, we need to find the value of \( \cot B \) given that \( A + B = 90^\circ \) and \( \tan A = \frac{3}{4} \).

### Step-by-Step Solution:

1. **Understand the Relationship Between A and B**:
Since \( A + B = 90^\circ \), we can express \( B \) in terms of \( A \):
\[ B = 90^\circ - A \]

2. **Use the Cotangent Identity**:
We know that:
\[ \cot B = \cot(90^\circ - A) \]
According to the co-function identity of trigonometric functions:
\[ \cot(90^\circ - A) = \tan A \]

3. **Substitute the Value of \( \tan A \)**:
We are given that \( \tan A = \frac{3}{4} \). Therefore:
\[ \cot B = \tan A = \frac{3}{4} \]

4. **Conclusion**:
Thus, the value of \( \cot B \) is:
\[ \cot B = \frac{3}{4} \]

### Final Answer:
\[ \cot B = \frac{3}{4} \]