Question

The sides of a triangle are in AP. If the angles A and C are the greatest and smallest angles, respectively, prove that 4(1 - cosA)(1 - cosC) = cosA + cosC.

Answer 1

We have 2b = a + c . Therefore,

2sinB =  sinA + sinC

Now,

From Eqs. (2) and (3), we get

cosA + cosC = 4(1 - cosA)(1 - cosC)