Question

If A,B,C are angles of a triangle and none of them is equal to
then prove that
2
tan A + tanB + tanC = tanA. tanB. tanC.​

Answer 1

Answer:

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

Step-by-step explanation:

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 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