Question

If a2 b2 and c2 are in A.p cota/2 cotb/2 and cotton c/2 are in ap

Answer 1

Answer:-cotC are in A.P.

We will show that if cotA, cotB and cotC are in AP then  will also be in AP.

Since cotA, cotB ,cotC are in AP then

2cotB = cotA + cotC

Put the trigonometry  ratios, we get following equation

-------------(1)

As we know,  (constant, suppose)

Thus, sinA = ka, sinB = kb, sinC = kc

and   ,

Put all the above values in eq. (1)  we get,

Thus,  are in A.P.