Question

If A+B=90° and cot B =¾ then the value of tan A=

• A. \(\frac{3}{4}\)
• B. \(\frac{4}{3}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{1}{4}\)

Answer 1

The Correct Option is A

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

1. Relationship Between Angles:
Since \( A + B = 90^\circ \), it follows that \( A \) and \( B \) are complementary angles. This means:

\[ A = 90^\circ - B \]

2. Using Complementary Angle Identities:
For complementary angles, the tangent of one angle is equal to the cotangent of the other angle. Specifically:

\[ \tan A = \cot B \]

3. Substituting the Given Value:
We are given that \( \cot B = \frac{3}{4} \). Therefore:

\[ \tan A = \cot B = \frac{3}{4} \]

4. Final Answer:
The value of \( \tan A \) is \( {\frac{3}{4}} \).