Question

If A+B+C=180° and CosA=CosB×CosC,prove that:TanB×TanC=2​

Answer 1

Explanation:

R.H.S.

= tanB+tanC

= (sinB/cosB)+(sinC/cosC)

= (sinBcosC+cosBsinC)/(cosB.cosC)

= sin(B+C)/cosA [cosA=cosB.cosC]

= sinA/cosA [A+B+C=pie, B+C=pie-A, sin(B+C)=sin(pie-A)= sinA]

= tanA = L.H.S. Proved.