for a=(2pi/2015)
what is the value of 
cosa*cos2a*cos3a*cos4a*.........................*cos1007a

Asked by SWETHA v | 18th Aug, 2014, 06:51: AM

Expert Answer:

G i e v n space a equals fraction numerator 2 straight pi over denominator 2015 end fraction  L e t space cos space a space. space cos space 2 a space. space cos space 3 a. space...... cos space 1007 a space equals space k space left parenthesis s a y right parenthesis  w e space k n o w space t h a t space cos space left parenthesis 2 straight pi minus straight theta right parenthesis equals cos space theta  s o space r e w r i t i n g space a b o v e space e q u a t i o n comma space w e space g e t  cos space left parenthesis 2 straight pi minus a right parenthesis. cos space left parenthesis 2 straight pi minus 2 a right parenthesis........ cos space left parenthesis 2 straight pi minus 1007 a right parenthesis equals k cos space 2 straight pi open parentheses 2014 over 2015 close parentheses. space cos space 2 straight pi open parentheses 2013 over 2015 close parentheses......... cos space 2 straight pi open parentheses 1008 over 2015 close parentheses equals straight k cos space straight pi open parentheses 4028 over 2015 close parentheses. space cosπ open parentheses 4026 over 2015 close parentheses........ cos space straight pi open parentheses 2016 over 2015 close parentheses equals straight k cos open parentheses 1 plus 2013 over 2015 close parentheses straight pi. space cos space open parentheses 1 plus 2011 over 2015 close parentheses straight pi..... cos open parentheses 1 plus 1 over 2015 close parentheses straight pi equals straight k open parentheses minus 1 close parentheses to the power of 1007 space cos space 2013 over 2015 straight pi. space cos space 2011 over 2015 straight pi....... cos space 1 over 2015 straight pi equals straight k cos space 2013 over 2015 straight pi. space cos space 2011 over 2015 straight pi....... cos space 1 over 2015 straight pi equals minus straight k

Answered by Dharma Teja | 18th Aug, 2014, 09:59: PM

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