02. If in a triangle ABC acos+ccos2S2 | A | = Sb, then the sides a, b

1.	02. If in a triangle ABC acos+ccos2S2 \| A \| = Sb, then the sides a, b and c22) 2(a) are in AP(b) are in GP(c) are in HP(d) satisfy a+ b c
Answer» cosC=2cos^2(C/2)-1 so, a(1+cosC)/2+c(1+cosA)/2=3b/2 a+acosC+c+ccosA=3b a+c+(acosC+ccosA)=3b Using By projection formula:(acosC+ccosA)=b a+c+b=3b a+c=2b This shows that a,b,c are in A.P. thanks

02. If in a triangle ABC acos+ccos2S2 | A | = Sb, then the sides a, b and c22) 2(a) are in AP(b) are in GP(c) are in HP(d) satisfy a+ b c

Answer»

cosC=2cos^2(C/2)-1

so, a(1+cosC)/2+c(1+cosA)/2=3b/2

a+acosC+c+ccosA=3b

a+c+(acosC+ccosA)=3b

Using By projection formula:(acosC+ccosA)=b

a+c+b=3b

a+c=2b

This shows that a,b,c are in A.P.

thanks