Q.
If a1,a2,…,an are in A.P., with common difference d≠0 then sum of the series sindcoseca1coseca2+coseca2coseca3+…+cosecan−1cosecanis
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a
seca1−secan
b
coseca1−cosecan
c
cota1−cotan
d
tana1−tanan
answer is C.
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Detailed Solution
sindcoseca1coseca2+coseca2coseca3+⋯+cosecan−1cosecan=sina2−a1sina1sina2+sina3−a2sina2sina3+⋯+sinan−an−1sinan−1sinan=cota1−cota2+cota2−cota3+⋯+cotan−1−cotan=cota1−cotan
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