What is the Formula of Tan (A + B + C) ?

Solution :

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

Proof :

We have,

tan (A + B + C) = tan((A + B) + C)

\(\implies\) tan (A + B + C) = \(tan (A + B) + tan C\over tan (A + B) tan C\)

\(\implies\) tan (A + B + C) = \({tan A + tan B\over 1 – tan A tan B} + tan C\over 1 – ({tan A + tan B\over 1 – tan A tan B})tan C\)

\(\implies\) tan (A + B + C) = \(tan A + tan B + tan C – tan A tan B tan C\over 1 – tan A tan B – tan B tan C – tan C tan A\)

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