## Solution to another S L Loney problem for IITJEE Advanced Mathematics

**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.**

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