If a1,a2,a3…..an is sequence of +Ve numbers which are in AP with  common difference 'd' &  sec a1sec a 2+sec⁡a2sec⁡a3+…………..+sec⁡an−1sec⁡an=

a2−a1=a3−a2=.....=an−1=d=1sindsina2−a1cosa1cosa2+sina3−a2cosa2cosa3+.....+sinan−an−1cos an−1cos8an=1sindtan a2−tana1+tana3−tan a2+....+tanan−tanan−1=tanan−tana1sind