Question

If A+B+C = 180° then find value of
$\frac{ \tan( \alpha ) + \tan( \beta ) + \tan( \gamma ) }{ \tan( \alpha ) \tan( \beta ) \tan( \gamma ) }$
​

Answer 1

Answer:

answer is 1

See the attachment

I think that will clear your all doubt

Answer 2

Answer:

1

Explanation:

A+B+C = π

A+B = π-C

tan(A+B) = tan(π-C)

tan(A+B) = -tanC

$\frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) } \: \: \: = - tan \gamma$

tanA + tanB = -tanC(1-tanAtanB)

tanA + tanB = -tanC +tanAtanBtanC

tanA + tanB + tanC / tanAtanBtanC = 1

hope it helps you buddy