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If tan A - tan B = 2 and cot B - cot A = 3, then what is the value of cot (A - B)?
1. 1/6
2. 5/6
3. 3/4
4. None of these

1 Answer

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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. 

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