Prove that tanA + tanB + tanC = tanA tanB tanC for any non-right angle triangle

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to prove that tan A + tan B + tan C = tan A*tan B*tan C for any non-right angle triangle.

For any triangle the sum of the angles is equal to 180 degrees. If we take a triangle ABC, A + B + C = 180 degrees.

...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

We have to prove that tan A + tan B + tan C = tan A*tan B*tan C for any non-right angle triangle.

For any triangle the sum of the angles is equal to 180 degrees. If we take a triangle ABC, A + B + C = 180 degrees.

A + B + C = 180 or 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 - tan A*tan B*tan C

=> tan A + tan B + tan C = tan A*tan B*tan C

This proves that tan A + tan B + tan C = tan A*tan B*tan C

Approved by eNotes Editorial Team