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Home / Doubts and Solutions/JEE/Mathematics

Prove that 

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Asked by Anish 9th July 2018, 11:29 AM
Answered by Expert
Answer:
begin mathsize 16px style sec straight pi over 11 sec fraction numerator 2 straight pi over denominator 11 end fraction sec fraction numerator 3 straight pi over denominator 11 end fraction sec fraction numerator 4 straight pi over denominator 11 end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 sin straight pi over 11 cross times fraction numerator 1 over denominator 2 sin straight pi over 11 cos begin display style straight pi over 11 end style end fraction cross times sec fraction numerator 2 straight pi over denominator 11 end fraction sec fraction numerator 3 straight pi over denominator 11 end fraction sec fraction numerator 4 straight pi over denominator 11 end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 sin straight pi over 11 cross times fraction numerator 1 over denominator sin fraction numerator 2 straight pi over denominator 11 end fraction end fraction cross times sec fraction numerator 2 straight pi over denominator 11 end fraction sec fraction numerator 3 straight pi over denominator 11 end fraction sec fraction numerator 4 straight pi over denominator 11 end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 squared sin straight pi over 11 cross times fraction numerator 1 over denominator 2 sin fraction numerator 2 straight pi over denominator 11 end fraction cos fraction numerator 2 straight pi over denominator 11 end fraction end fraction sec fraction numerator 3 straight pi over denominator 11 end fraction sec fraction numerator 4 straight pi over denominator 11 end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 squared sin straight pi over 11 cross times fraction numerator 1 over denominator sin fraction numerator 4 straight pi over denominator 11 end fraction cross times cos fraction numerator 4 straight pi over denominator 11 end fraction end fraction cross times sec fraction numerator 3 straight pi over denominator 11 end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 cubed sin straight pi over 11 cross times fraction numerator 1 over denominator 2 sin fraction numerator 4 straight pi over denominator 11 end fraction cross times cos fraction numerator 4 straight pi over denominator 11 end fraction end fraction cross times sec fraction numerator 3 straight pi over denominator 11 end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 cubed sin straight pi over 11 cross times fraction numerator 1 over denominator sin fraction numerator 8 straight pi over denominator 11 end fraction end fraction cross times sec fraction numerator 3 straight pi over denominator 11 end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 cubed sin straight pi over 11 cross times fraction numerator 1 over denominator sin fraction numerator 8 straight pi over denominator 11 end fraction cos fraction numerator 3 straight pi over denominator 11 end fraction end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 cubed sin straight pi over 11 cross times fraction numerator 1 over denominator sin open parentheses straight pi minus fraction numerator 3 straight pi over denominator 11 end fraction close parentheses cos fraction numerator 3 straight pi over denominator 11 end fraction end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 cubed sin straight pi over 11 cross times fraction numerator 1 over denominator sin fraction numerator 3 straight pi over denominator 11 end fraction cos fraction numerator 3 straight pi over denominator 11 end fraction end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 to the power of 4 sin straight pi over 11 cross times fraction numerator 1 over denominator 2 sin fraction numerator 3 straight pi over denominator 11 end fraction cos fraction numerator 3 straight pi over denominator 11 end fraction end fraction sec fraction numerator 5 straight pi over denominator 11 end fraction equals 2 to the power of 4 sin straight pi over 11 cross times fraction numerator 1 over denominator sin fraction numerator 6 straight pi over denominator 11 end fraction cos fraction numerator 5 straight pi over denominator 11 end fraction end fraction equals 2 to the power of 4 sin straight pi over 11 cross times fraction numerator 1 over denominator sin open parentheses straight pi minus fraction numerator 5 straight pi over denominator 11 end fraction close parentheses cos fraction numerator 5 straight pi over denominator 11 end fraction end fraction equals 2 to the power of 4 sin straight pi over 11 cross times fraction numerator 1 over denominator sin fraction numerator 5 straight pi over denominator 11 end fraction cos fraction numerator 5 straight pi over denominator 11 end fraction end fraction equals 2 to the power of 5 sin straight pi over 11 cross times fraction numerator 1 over denominator 2 sin fraction numerator 5 straight pi over denominator 11 end fraction cos fraction numerator 5 straight pi over denominator 11 end fraction end fraction equals 2 to the power of 5 sin straight pi over 11 cross times fraction numerator 1 over denominator sin begin display style fraction numerator 10 straight pi over denominator 11 end fraction end style end fraction equals 2 to the power of 5 sin straight pi over 11 cross times fraction numerator 1 over denominator sin begin display style open parentheses straight pi minus straight pi over 11 close parentheses end style end fraction equals 2 to the power of 5 sin straight pi over 11 cross times fraction numerator 1 over denominator sin begin display style fraction numerator begin display style straight pi end style over denominator begin display style 11 end style end fraction end style end fraction equals 2 to the power of 5 end style
Answered by Expert 10th July 2018, 3:44 PM
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