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Nilai cos 7 2 π ​ + cos 7 4 π ​ + cos 7 6 π ​ = ...

Nilai 

  1. begin mathsize 12px style 1 half end style

  2. begin mathsize 12px style square root of 2 minus square root of 2 end root end style

  3. begin mathsize 12px style 1 half square root of 2 end style

  4. begin mathsize 12px style negative 1 half end style

  5. begin mathsize 12px style negative 1 half square root of 2 end style

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begin mathsize 12px style open parentheses cos fraction numerator 2 straight pi over denominator 7 end fraction plus cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 7 end style end fraction plus cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 7 end style end fraction close parentheses times fraction numerator sin begin display style straight pi over 7 end style over denominator sin straight pi over 7 end fraction  equals fraction numerator cos fraction numerator 2 straight pi over denominator 7 end fraction times sin straight pi over 7 plus cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 7 end style end fraction times sin straight pi over 7 plus cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 7 end style end fraction times sin straight pi over 7 over denominator sin straight pi over 7 end fraction    Ingat space rumus colon  2 space cos space A space sin space B equals sin open parentheses A plus B close parentheses minus sin open parentheses A minus B close parentheses  cos space A space sin space B equals 1 half sin open parentheses A plus B close parentheses minus sin open parentheses A minus B close parentheses    maka colon  fraction numerator begin display style 1 half end style open parentheses sin begin display style fraction numerator 3 straight pi over denominator 7 end fraction end style minus sin straight pi over 7 close parentheses plus 1 half open parentheses sin fraction numerator 5 straight pi over denominator 7 end fraction minus sin fraction numerator 3 straight pi over denominator 7 end fraction close parentheses plus 1 half open parentheses sin straight pi minus sin fraction numerator 5 straight pi over denominator 7 end fraction close parentheses over denominator sin straight pi over 7 end fraction  equals fraction numerator begin display style sin fraction numerator 3 straight pi over denominator 7 end fraction minus sin straight pi over 7 plus sin fraction numerator 5 straight pi over denominator 7 end fraction minus sin fraction numerator 3 straight pi over denominator 7 end fraction plus sinπ minus sin fraction numerator 5 straight pi over denominator 7 end fraction end style over denominator 2 space sin straight pi over 7 end fraction  equals fraction numerator begin display style sin fraction numerator 3 straight pi over denominator 7 end fraction minus sin straight pi over 7 plus sin fraction numerator 5 straight pi over denominator 7 end fraction minus sin fraction numerator 3 straight pi over denominator 7 end fraction plus sinπ minus sin fraction numerator 5 straight pi over denominator 7 end fraction end style over denominator 2 space sin straight pi over 7 end fraction  equals fraction numerator begin display style sinπ minus sin straight pi over 7 end style over denominator 2 space sin straight pi over 7 end fraction  equals fraction numerator begin display style 0 minus sin straight pi over 7 end style over denominator 2 space sin straight pi over 7 end fraction  equals fraction numerator begin display style negative sin straight pi over 7 end style over denominator 2 space sin straight pi over 7 end fraction  equals negative 1 half end style

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