ABC-is-a-non-right-triangle-1-Demonstrate-that-tan-A-B-tanC-1-By-using-tan-A-B-tanA-tanB-1-tanA-tanB-prove-that-tanA-tanB-tanC-tanAtanBtanC-please-i-nee

Question Number 77123 by mathocean1 last updated on 03/Jan/20

ABC is a non - right triangle .

1) Demonstrate that

\tan (\hat{A} + \hat{B}) = - \tan \hat{C} .

1) By using \tan (\hat{A} + \hat{B}) = \frac{\tan \hat{A} + \tan \hat{B}}{1 - \tan \hat{A t a n} \hat{B}}

prove that \tan \hat{A} + \tan \hat{B} + \tan \hat{C} = tanAtanBtanC

please i need your help

Answered by john santu last updated on 03/Jan/20

(1) A + B = π - C

\tan (A + B) = \tan (π - C)

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

Commented by john santu last updated on 03/Jan/20

(2) \tan (A + B) + \tan C = 0

\frac{\tan A + \tan B}{1 - \tan A \times \tan B} + \tan C = 0

\tan A + \tan B + \tan C - \tan A \times \tan B \times \tan C = 0

\tan A + \tan B + \tan C = \tan A \times \tan B \times \tan C

Commented by mathocean1 last updated on 03/Jan/20

thank you sir \dots