If `a_1,a_2,a_3, ,a_n` are in A.P. with common difference `d(where d!=0)` , then the sum of series. sin`d` `d(cos e ca_1cos e ca_2+cos e ca_2cos e ca_3+=cos e ca_(n-1)cos e ca_n)` is equal to`cota_1-cota_ndot`

Explanation

Given `a_1, a_2, …. , a_n `are in A.P with common difference, d.


So `d = a_2-a_1 = a_3-a_2 = a_4-a_3 ….= a_n-a_n-1`


`sin d(cosec a_1 . cosec a_2 + cosec a_2 . cosec a_3 + ….. + cosec a_n-1 cosec a_n) `


`= (sin d/sin a_1 sin a_2) + (sin d/sin a_2 sin a_3) + …..(sin d/sin a_n-1 sin a_n)`


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