If `a_1,a_2,a_3,...a_n` are in A.P with common difference `d` then find the sum of the following series `sind(coseca_1coseca_2+coseca_2coseca_3+....coseca_(n-1)coseca_n)`

If a_1,a_2,a_3, ,a_n are in A.P. with common difference d(w h e r ed!=0) , then the sum of series. sind (coseca_1 coseca_2+coseca_2 coseca_3 +....+ coseca_(n-1) cos e ca_n) is equal to cot a_1-cot a_n

If a_1, a_2, a_3,...a_n are in A.P with common difference d !=0 then the value of sind(coseca_1 coseca_2 +cosec a_2 cosec a_3+...+cosec a_(n-1) cosec a_n) will be

if a_(1), a_(2) , a_(3),"……",a_(n) are in A.P. with common difference d, then the sum of the series : sin d [coseca_(1) coseca_(2) + cosec a_(2) cosec a_(3) + "…."cosec a_(n-1) cosec a_(n)] is :

If a_1, a_2,a_3,..........., a_n are in A.P. with common difference d, prove that : sin d [cosec a_1 coseca_2+ coseca_2coseca_3+....coseca_(n-1)coseca_n]= cot a_1-a_n .

If a_(1),a-(2),a_(3),………….a_(n) are in A.P. with common differecne d, prove that sin [cosec a_(1)coseca_(2)+cosec a_(2)cosec a_(3)+………….+cosec a_(n-1)cosec a_(n)]=cota_(1)-cota_(n) .

If a_1,a_2,…………..a_n are in AP with common difference d ne 0 then find (sin d) [sec a_1 sec a_2+ sec a_2 sec a_3+…….+sec a_(n-1) sec a_n]

4.If a, a, ag.....an are in A.P. and commondifference is d then the value ofsind(coseca, coseca.y + coseca, cosecaz+ ... cosecdn-1 cosecan)will be-(1) seca1 - Secon (2) coseca1 - cosecan(3) cota1-cotan(4) tandi-tanan

If a_1,a_2,a_3,...,a_n be in AP whose common difference is d then prove that sum_(i=1)^n a_ia_(i+1)=n{a_1^2+na_1d+(n^2-1)/3 d^2} .

Prove the following identities: (1+secA+tanA)(1-cosecA+cotA)=2