If tan A = 3/4 and tan B = -12/5, then cot (A - B) is1. 12. 23. 34. No

1.	If tan A = 3/4 and tan B = -12/5, then cot (A - B) is1. 12. 23. 34. None of these
Answer» Correct Answer - Option 4 : None of these Concept: tan(A - B) = \(\rm \frac{tanA-tan B}{1+tan AtanB}\) Calculation: We know, tan(A - B) = \(\rm \frac{tanA-tan B}{1+tan AtanB}\) ∴cot(A - B) = \(\rm \frac{1+tan AtanB}{tanA-tan B}\) \(=\rm \frac{1+\frac{3}{4}\times \frac{-12}{5}}{\frac 3 4 + \frac{12}{5}}\) \(=\rm \frac{1-\frac{36}{20}}{\frac {63}{20}}\) \(=\rm \frac{-16}{20}\times \frac {20}{63}=\frac{-16}{63}\) Hence, option (4) is correct.

If tan A = 3/4 and tan B = -12/5, then cot (A - B) is1. 12. 23. 34. None of these

Answer» Correct Answer - Option 4 : None of these

Concept:

tan(A - B) = \(\rm \frac{tanA-tan B}{1+tan AtanB}\)

Calculation:

We know, tan(A - B) = \(\rm \frac{tanA-tan B}{1+tan AtanB}\)

∴cot(A - B) = \(\rm \frac{1+tan AtanB}{tanA-tan B}\)

\(=\rm \frac{1+\frac{3}{4}\times \frac{-12}{5}}{\frac 3 4 + \frac{12}{5}}\)

\(=\rm \frac{1-\frac{36}{20}}{\frac {63}{20}}\)

\(=\rm \frac{-16}{20}\times \frac {20}{63}=\frac{-16}{63}\)

Hence, option (4) is correct.