P r o v e space t h a t : cos squared A space plus space cos squared open parentheses A plus straight pi over 3 close parentheses space plus space cos squared open parentheses A minus straight pi over 3 close parentheses space equals space 3 over 2

Asked by Olivia Adhikary | 4th Aug, 2014, 12:43: PM

Expert Answer:

C o n s i d e r space t h e space l e f t space h a n d space s i d e space o f space t h e space g i v e n space e q u a t i o n : cos squared A plus cos squared open parentheses A plus straight pi over 3 close parentheses plus cos squared open parentheses A minus straight pi over 3 close parentheses equals 3 over 2 equals fraction numerator 1 plus cos 2 A over denominator 2 end fraction plus fraction numerator 1 plus cos 2 open parentheses A plus straight pi over 3 close parentheses over denominator 2 end fraction plus fraction numerator 1 plus cos 2 open parentheses A minus straight pi over 3 close parentheses over denominator 2 end fraction equals fraction numerator 1 plus cos 2 A over denominator 2 end fraction plus fraction numerator 1 plus cos open parentheses 2 A plus fraction numerator 2 straight pi over denominator 3 end fraction close parentheses over denominator 2 end fraction plus fraction numerator 1 plus cos open parentheses 2 A minus fraction numerator 2 straight pi over denominator 3 end fraction close parentheses over denominator 2 end fraction equals fraction numerator 1 plus cos 2 A plus 1 plus cos open parentheses 2 A plus fraction numerator 2 straight pi over denominator 3 end fraction close parentheses plus 1 plus cos open parentheses 2 A minus fraction numerator 2 straight pi over denominator 3 end fraction close parentheses over denominator 2 end fraction equals fraction numerator 1 plus cos 2 A plus 1 plus cos 2 A cos fraction numerator 2 straight pi over denominator 3 end fraction minus sin 2 A sin fraction numerator 2 straight pi over denominator 3 end fraction plus 1 plus cos 2 A cos fraction numerator 2 straight pi over denominator 3 end fraction plus sin 2 A sin fraction numerator 2 straight pi over denominator 3 end fraction over denominator 2 end fraction equals fraction numerator 1 plus cos 2 A plus 1 plus cos 2 A cross times open parentheses begin display style fraction numerator minus 1 over denominator 2 end fraction end style close parentheses plus 1 plus cos 2 A open parentheses fraction numerator minus 1 over denominator 2 end fraction close parentheses over denominator 2 end fraction equals fraction numerator 3 plus cos 2 A minus cos 2 A over denominator 2 end fraction equals 3 over 2 equals R. H. S. H e n c e space p r o v e d.

Answered by Vimala Ramamurthy | 5th Aug, 2014, 09:59: AM

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