a-maths~

a/sinA = b/sinB = c/sinC = ka = ksinA,b = ksinB,c = ksinC

a^2 = b^2 + c^2 - 2bc cosA <=> (b^2 + c^2 - a^2)/2bc = cosA LHS= (b²+c²-a²)/2bc= [(ksinB)^2+(ksinC)^2-(ksinA)^2]/2(ksinB)(ksinC)=[(sinB)^2+(sinC)^2-(sinA)^2]/2(sinB)(sinC)= [(sinB)^2+(sinC)^2-sin(180-(B+C))^2]/2(sinB)(sinC)= [(sinB)^2+(sinC)^2-sin(B+C)^2]/2(sinB)(sinC)= [(sinB)^2+(sinC)^2-(sinBcosC+cosBsinC)^2]/2(sinB)(sinC)= [(sinB)^2+(sinC)^2-(sinBcosC)^2-(cosBsinC)^2-2sinBsinCcosBcosC]/2(sinB)(sinC)= [2(sinB)^2(sinC)^2 - 2sinBsinCcosBcosC]/2(sinB)(sinC)= sinBsinC - cosBcosC

= -cos(B + C)= cos(180 - (B + C))= cosA= RHS

Hope it helps !!!