You are here:

Advanced Math/trig identies

Advertisement

Expert: Robi Bhattacharjee - 2/2/2009


Question
a non right triangle:
tan(a)+tan(b)+tan(c) =tan(a)tan(b)tan(c)
I need guidance on proof. Not sure how to use Eulers eq

Answer
Hi Don,

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

LHS= tan(a) + tan(b) - tan(a+b)    since c+a+b=pi

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

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

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

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

= tan(a)tan(b)tan(c)


I hope this helps,
Robi

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

©2012 About.com, a part of The New York Times Company. All rights reserved.