Question

Question : If a+b+c= 180 , then show that :
tan(a)+tan(b)+tan(c)= tan(a)tan(b)tan(c)​

Answer 1

Here's the Solution:

Given ,

a + b + c = 180

$a + b = 180 - c \\ \\ = > \tan(a + b) = \tan(180 - c) \\ \\ = > \tan(a + b) = - \tan(c) \\ \\ = > \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) } = - \tan(c) \\ \\ = > \tan(a) + \tan(b) = - \tan(c) + \tan(a)\tan(b) \tan(c) \\ \\ = > \tan(a) + \tan(b) + \tan(c) = \tan(a) \tan(b) \tan(c) \\ \\ hence \: shown$

Answer 2

Heya Brainly User !

Your Solution :

Given ,

a + b + c = 180

=> a + b = 180 - c

=>tan(a + b ) = tan(180 - c)

=> [tan(a) +tan(b)]/[1-tan(a)tan(b)]= -tan (c)

=>tan(a)+tan(b) = -tan(c){1-tan(a)tan(b)}

=> tan(a)+tan(b) = -tan(c)+tan(a)tan(b)tan(c)

=>tan(a)+tan(b)+tan(c) = tan(a)tan(b)tan(c)

Proved ✔✔✔✔✔