Correct Answer - Option 2 : 5/6
Concept:
cot ( A - B ) = \(\rm \frac{\cot A \cot B+1}{\cot B-\cot A}\)
Calculation:
Given:
tan A - tan B = 2
cot B - cot A = 3 ....(1)
Now, tan A - tan B = 2
⇒ \(\rm \frac{1}{\cot A}-\frac{1}{\cot B}= 2\)
⇒ \(\rm \frac{\cot B-\cot A }{\cot A \cot B } = 2 \)
From eq. ( i ), we get
cot A.cot B = \(\frac{3}{2}\)
As we know that , cot ( A - B ) = \(\rm \frac{\cot A \cot B+1}{\cot B-\cot A}\)
cot ( A- B ) = \(\rm \frac{\frac{3}{2}+1}{3}\)
⇒ cot ( A - B ) = \(\frac{5}{6}\)
The correct option is 1.