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