Question

if A+B+C =180 AND COSA=COSB.COSC THEN PROVE TANB.TANC=2​ how to know to use which function ​

Answer 1

$answer$

A = 180 - ( b+c )

so,

Cosa = - cos ( b + c) = - (cosb cosc - sinb sinc)

= - cosb cosc + sinb sinc

But cosa =cosb. cos c so

-cosb cosc + sinb sinc = cosb cosc and

Therefore,

sinb sinc = 2 cosb cosc

Dividing through by cosb cosc we get tanb tanc = 2 q.e.d

hope it helps you