What is the Formula of Cot (A - B) ?

Solution :

The formula of cot (A – B) is \(cot A cot B + 1\over cot B – cot A\).

Proof : We have,

cot (A – B) = \(cos (A – B)\over sin(A – B)\)

Using sin (A – B) and cos (A – B) formula,

cot (A – B) = \(cos A cos B + sin A sin B\over sin A cos B – cos A sin B\)

Dividing the numerator and denominator by sin A sin B,

cot (A – B) = \(cot A cot B + 1\over cot B – cot A\)