Question

if tan A - tan B = x and cot B - cot A =y then cot ( A - B) equals to

Answer 1

we have tan A – tanB = sin (A – B) / cosA cosB  & cot B – cot A = sin (A – B)/ sinA sin B

1/x + 1/y = cosA cosB /sin(A – B) + sinA sinB / sin (A – B)

=(cosA cosB + sinA sinB) /sin (A – B)

= cos (A – B) / sin (A – B) = cot (A – B)

 

Ans:  cot (A – B) = 1/x + 1/y