Question

What is the formula for
TanA - TanB - TanC

Answer 1

TanA - TanB - TanC
= tanA - (tanB + tanC)
=tanA - (tan(b + c)(1 - tanbtanc))
= sinA/cosA  - (sin(b + c)/cos(b + c)((cosbcosc - sinasinb)/cosbcosc))
= sinA/cosA  - (sin(b + c)/cos(b + c)((cos(b+c))/cosbcosc))
= sinA/cosA  - sin(b + c)/(cosbcosc)
= {sinacosbcosc  - sin(b +c)cosa}/cosacosbcosc

Answer 2

$tanA-tanB-tanC=\frac{sinA}{cosA}-\frac{sinB}{cosB}-\frac{sinC}{cosC}\\\\=\frac{sinAcosBcosC-sinBcosAcosC-sinCcosAcosB}{cosAcosBcosC}$