Question

If a2,b2,c2 are in AP then prove that cotA/2,cotB/2,cotC/2 are also in A.P

Answer 1

Answer:

Let us consider that cotA,cotB,cotC are in AP and prove that a2,b2,c2 are in AP.

we know that cotA=\frac{b^{2}+c^{2}-a^{2}}{4(area of triangle)} and similarly cotB,cotC..

by considering that cotA,cotB,cotC are inAP,we get

2(c2+a2-b2)=(b2+c2-a2)+(b2+a2-c2),

by simplifying,we get

2b2=a2+c2,

\thereforea2,b2,c2 are in AP