If tan A - tan B = x and cot B - cot A =y , then what is cot ( A -B) equal to ?

Options

A. `(1)/(y)-(1)/(x)`
B. `(1)/(x)-(1)/(y)`
C. `(1)/(x)+(1)/(y)`
D. `-(1)/(x)-(1)/(y)`

Answer

C

Explanation

Let tan A- tan B = x and cot B - cot A = y.
`rArr(1)/(tanB)-(1)/(tanA)=y`
`rArr(tanA-tanB)/(tanAtanB)=yrArr(x)/(tanAtanB)=y`
Consider cot (A -B) `=((1)/(tan(A-B)))`
`=(1+tanAtanB)/(tanA-tanB)=(1+(x)/(y))/(x)=(y+x)/(xy)=(1)/(x)+(1)/(y)`.