If a1,a2,a3,…….an are in A.P with common difference d≠0, then sum of the  series sin⁡dsec⁡a1sec⁡a2+sec⁡a2sec⁡a3+………+sec⁡an−1sec⁡an is

As a1,a2,a3,…………an−1,an are in A.P hence d=a2−a1=a3−a2=……..=an−an−1sin⁡dsec⁡a1sec⁡a2+sec⁡a2sec⁡a3+…………….+sec⁡an−1sec⁡an=sin⁡a2−a1cos⁡a1cos⁡a2+sin⁡a3−a2cos⁡a2cos⁡a3+…………..+sin⁡an−an−1cos⁡an−1cos⁡an=tan⁡a2−tan⁡a1+tan⁡a3−tan⁡a2+…………+tan⁡an−tan⁡an−1=tan⁡an−tan⁡a1