Question

If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.

पर्याय

• `1/x + y`

• `1/(xy)`

• `1/x - 1/y`

• `1/x + 1/y`

Answer 1

If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = `underlinebb(1/x + 1/y)`.

Explanation:

cot(A – B) = `1/(tan(A - B))`

= `(1 + tan A tan B)/(tan A - tan B)`

= `1/(tan A - tan B) + (tan A tan B)/(tan A - tan B)`

= `1/x + 1/y`