Question

tan A = 1/2,tan B=2/7 Find cot (A-B)​

Answer 1

Answer:

cot (A-B) = 16/3

Explanation:

Given that

Tan A =  1/2

Tan B = 2/7

We know

cot Ф = 1/ Tan Ф

Therefore, cot A = 2

                  cot B = 7/2

By identity

Cot (α-β) = cot α cot β + 1 / cot β - cot α

Substituting the above values.

⇒cot (A-B) = cot A cot B + 1 / cot B - cot A

⇒cot (A-B) = 2(7/2) + 1 / 7/2 - 2

⇒cot (A-B) = 7 + 1 / (7 - 2(2)/2)

⇒cot (A-B) = 8/ (7-4/2)

⇒cot (A-B) = 8/(3/2)

⇒cot (A-B) = 16/3

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