Mathematics - Properties of Triangle Question with Solution | TestHub

cos A+cos B=2(1-cos C)=4 ${\sin }^2\left(C/2\right)$. By cos A+cos B=2sin(C/2)cos((A-B)/2), cancel 2sin(C/2)>0 to obtain cos((A-B)/2)=2sin(C/2). Multiply by 2cos(C/2): sin A+sin B=2sin C. The sine rule gives a+b=2c, so a,c,b are in A.P.