Question

if cosA=cosB.cosC,then prove tanA=tanB.tanC​ and A+B+C=180

Answer 1

Answer:

cos a = - cos(b+c) = - (cos b cos c - sin b sin c) = - cos b cos c + sin b sin c

But cos a =cos b cos c so

- cos b cos c + sin b sin c = cos b cos c and therefore

sin b sin c = 2 cos b cos c

Dividing through by cos b cos c we get

tan b tan c = 2 q.e.d

Step-by-step explanation: