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Home / Doubts and Solutions/JEE/Mathematics

Prove that

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Asked by Anish 6th July 2018, 10:21 PM
Answered by Expert
Answer:
begin mathsize 16px style cos straight pi over 13 cos fraction numerator begin display style 2 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator 1 over denominator 2 sin straight pi over 13 end fraction open parentheses 2 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction close parentheses cos fraction numerator begin display style 2 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 squared sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction cross times open parentheses 2 sin fraction numerator begin display style 2 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 2 straight pi end style over denominator begin display style 13 end style end fraction close parentheses cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 squared sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction cross times sin fraction numerator begin display style 4 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 cubed sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction cross times open parentheses 2 sin fraction numerator begin display style 4 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 13 end style end fraction close parentheses cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 cubed sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction cross times sin fraction numerator 8 straight pi over denominator 13 end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 cubed sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction cross times sin open parentheses straight pi minus fraction numerator 5 straight pi over denominator 13 end fraction close parentheses cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 cubed sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction sin fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 4 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction 2 open parentheses sin fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 5 straight pi end style over denominator begin display style 13 end style end fraction close parentheses cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 4 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction sin fraction numerator 10 straight pi over denominator 13 end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 5 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction 2 sin open parentheses straight pi minus fraction numerator 3 straight pi over denominator 13 end fraction close parentheses cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 5 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction 2 sin fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 3 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 5 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction sin fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 6 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction 2 sin fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 13 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 6 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction sin fraction numerator 12 straight pi over denominator 13 end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 6 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction sin open parentheses straight pi minus straight pi over 13 close parentheses equals fraction numerator begin display style 1 end style over denominator begin display style 2 to the power of 6 sin fraction numerator begin display style straight pi end style over denominator begin display style 13 end style end fraction end style end fraction sin straight pi over 13 equals 1 over 64 end style
Answered by Expert 10th July 2018, 4:06 PM
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