Question

If tan A - tan B = x and cot B - cot A = y, then
cot (A - B) =​

Answer 1

Answer:

1/x + 1/y

Step-by-step explanation:

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Answer 2

Answer:

$\boxed {cot(A - B) = \frac{y+1}{xy}}$

Step-by-step explanation:

Given :

tan A - tan B = x ____(1)

cot B - cot A = y _____(2)

we know that cotα = 1/tanα

Hence, In (2)

cot B - cot A = y

$\frac{1}{tanB} - \frac{1}{tanA} = \frac{tanA - tanB}{tanA.tanB}$ = y

From (1),

$y = \frac{x}{tanA.tanB}$

$y = cotAcotB \times x\\Hence, \ cotAcotB = \frac{y}{x}$ ____(3)

Now, to find cot (A - B) =

We know that,

$\cot(A-B) = \frac{cotBcotA + 1}{cotB-cotA}$

Hence, from the formula, substituting from (2) and (3)

$\large{\text{ cot(A - B) = \frac{\frac{y}{x} + 1}{y} }} \\\\=> cot(A - B) = \frac{y+1}{xy}$

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