If (a1,a2,a3......an) are in A>P> with common difference d. then the sum of the series: sin d [cosec a1.cosec a2 + cosec a2.cosec a3 +........+ cosec a(n-1).cosec an ] is what ??

Given: a1, a2, a3, ..... an are in A.P. with common difference d

Then d = (a2a1) = (a3a2) ......  (an an-1)

Now,

sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ..... cosec an-1 cosec an)

= cot a1 – cot an

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