Question

Given that A= B+C, prove that Tan A -tan B- tanC =tanAtanBtanC

Answer 1

To prove -

If A = B+C then

tanA - tanB - tanC = tanA.tanB.tanC.

Proof -

Clearly

A = B+C

tanA = tan( B+C)

We know that

tan( a + b) =( tan a+ tan b) /1- tan a .tan b

So,

→tan A =( tan B+ tan C)/ 1 - tanB. tanC

→tanA( 1 - tanB tanC) = tanB +tanC

→tanA - tanA tanB tanC = tan B + tan C

→tanA - tanB - tanC = tanA.tanB.tanC

Hence proved .