# 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) = $$cot A cot B + 1\over cot B – cot A$$

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