Expansion of tan (A + B + C)

We will learn how to find the expansion of tan (A + B + C). By using the formula of tan (α + β) we can easily expand tan (A + B + C).

Let us recall the formula of tan (α + β) = tan α + tan β/1 - tan α tan β.

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

= tan (A + B) + tan C/1 - tan (A + B) tan C, [applying the formula of tan (α + β)]

= tan A + tan B/(1 - tan A tan B) + tan C /1 - (tan A + tan B)/1 - tan A tan B ∙ tan C, [again applying the formula of tan (α + β)]

= tan A + tan B + tan C - tan A tan B tan C/ 1 - tan A tan B- tan C tan A - tan B tan C

Therefore, the expansion of tan (A + B + C) = tan A + tan B + tan C - tan A tan B tan C/ 1 - tan A tan B- tan C tan A - tan B tan C.

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