Question

If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is

Answer 1

4) (1/x) + (1/y)

Solution:

Given,

tan A – tan B = x….(i)

cot B – cot A = y

(1/tan B) – (1/tan A) = y

(tan A – tan B)/ (tan A tan B) = y

x/ tan A tan B = y {from (i)}

tan A tan B = x/y….(ii)

cot(A – B) = 1/tan(A – B)

= (1 + tan A tan B)/ (tan A – tan B)

= [1 + (x/y)]/ x {from (i) and (ii)}

= (y + x)/xy

= (y/xy) + (x/xy)

= (1/x) + (1/y)

Answer 2

tan A - tan B = x

cot B - cot A = y

=> 1/tanB - 1/tanA = y

=> (tanA - tanB)/tanB.tanA = y

=> x/y = tanA.tanB

Cot(A - B) = 1/(tan(A - B)) = (1 + tanA.TanB)/(TanA - TanB)

= (1 + x/y)/(x)

= (y + x)/xy

= (x + y)/xy

cot (A-B) = (x + y)/xy