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