ManipulationHardQuestion 200040
Question
If tan A − tan B = x and cot B − cot A = y, then cot(A − B) equals:
- A1/x + 1/yCorrect
- B1/x − 1/y
- Cx + y
- D(x+y)/(xy)
Correct answer
1/x + 1/y
Explanation
cot(A−B) = (cot A cot B + 1)/(cot A − cot B). Given: cot B − cot A = y → cot A − cot B = −y. Also tan A − tan B = x. Since cot A − cot B = −(tan B − tan A)/(tan A tan B), working through: cot(A−B) = 1/x + 1/y.