Exercise XXVII. Problem #32. The sides of a triangle are in AP and the greatest and least angles are and
. Prove that
Proof:
Let a, b, c be in AP. Hence, , which in turn implies c is greatest and a is the least.
Hence, and
.
Want:
Given:
. Hence,
Now, we have and this is equal to the following:
.
Also, similarly, we have the following:
but it is given that , hence,
,
. So the above expression changes to
.
QED.