Question

If tan A-tan B =x and cot B-cot A = y, the cot(A - B)is equal to​

Answer 1

Answer:

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

Step-by-step explanation:

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

Answer 2

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

Step-by-step explanation:

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

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