Question

If A+B+C=180 then prove tan A+tan B+tanC=tan A.tanB.tanC

Answer 1

hay!!

Dear friend!!

According to the question we know that

A+B+C =180

So,

=> A+B=180-C

Let multiply by tan we found that

=> tan(A+B) = tan(180-C)

$\frac{(tana + tanb)}{(1 - tana \: tanb)} = - tanc$

=> tanA+tanB = -tanC(1-tanA tanB)

=> tanA+tanB= - tanC+tanA tanB tanC

=> tanA +tanB +tanC = tanA tanB tanC

Hence proved

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Answer 2

Answer:

Proved

Step-by-step explanation:

Check image.

valid for all cases. Even if C is obtuse when tan(180-C) is not negative.

Note : Equation is not valid for right angles. (tan90°= infinity