The formula of (cot A - B) is?

Trigonometry deals with the measurement of angles and helps us study the relationship between the sides and angles of a right-angled triangle. Trigonometric identities are equations that relate different trigonometric functions and are true for any value of the variable that is there in the domain.

Answer: The formula of (cot A - B) is (cot A cot B + 1) / (cot B – cot A)

Let's derive the formula of (cot A - B).

Explanation:

We know that,

cot (A – B) = 1/ tan (A- B) [Since, cot x = 1 / tan x] -------------- (1)

Now, we know that,

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

⇒ 1/ tan (A- B) = (1 + tan A tan B) / (tan A - tan B) ---------------- (2)

Substituting the value of (2) in (1) we get,

⇒ cot (A - B) = (1 + tan A tan B) / (tan A - tan B) ---------------- (3)

We know that, tan x = 1 / cot x

Thus, replacing tangent values with cotangent values in (3)

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

On solving,

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

Hence, the formula of (cot A - B) is (cot A cot B + 1) / (cot B – cot A)