# What is the Formula of Tan (A – B) ?

## Solution :

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

Proof : We have,

tan (A – B) = $$sin (A – B)\over cos(A – B)$$

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

tan (A – B) = $$sin A cos B – cos A sin B\over cos A cos B + sin A sin B$$

Dividing the numerator and denominator by cos A cos B,

tan (A – B) = $$tan A – tan B\over 1 + tan A tan B$$.

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