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Home / Doubts and Solutions/JEE/Mathematics

Prove that

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Asked by Anish 6th July 2018, 10:18 PM
Answered by Expert
Answer:
begin mathsize 16px style sin straight pi over 14 sin fraction numerator 3 straight pi over denominator 14 end fraction sin fraction numerator 5 straight pi over denominator 14 end fraction equals sin fraction numerator begin display style straight pi end style over denominator begin display style 14 end style end fraction sin open parentheses fraction numerator begin display style straight pi end style over denominator 2 end fraction minus fraction numerator begin display style 3 straight pi end style over denominator begin display style 14 end style end fraction close parentheses sin open parentheses fraction numerator begin display style straight pi end style over denominator 2 end fraction minus fraction numerator begin display style 5 straight pi end style over denominator begin display style 14 end style end fraction close parentheses equals sin fraction numerator begin display style straight pi end style over denominator begin display style 14 end style end fraction cos open parentheses fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction close parentheses cos open parentheses fraction numerator begin display style 2 straight pi end style over denominator 14 end fraction close parentheses equals fraction numerator 1 over denominator begin display style 2 end style cos begin display style fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction cross times sin fraction numerator begin display style straight pi end style over denominator begin display style 14 end style end fraction cross times 2 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction cross times cos open parentheses fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction close parentheses cos open parentheses fraction numerator begin display style 2 straight pi end style over denominator 14 end fraction close parentheses equals fraction numerator begin display style 1 end style over denominator begin display style 2 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction cross times sin fraction numerator 2 straight pi over denominator 14 end fraction cos open parentheses fraction numerator begin display style 2 straight pi end style over denominator 14 end fraction close parentheses cross times cos open parentheses fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction close parentheses equals fraction numerator begin display style 1 end style over denominator begin display style 2 cross times 2 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction cross times 2 sin fraction numerator begin display style 2 straight pi end style over denominator begin display style 14 end style end fraction cos open parentheses fraction numerator begin display style 2 straight pi end style over denominator 14 end fraction close parentheses cross times cos open parentheses fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction close parentheses equals fraction numerator begin display style 1 end style over denominator begin display style 2 cross times 2 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction sin fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction cos open parentheses fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction close parentheses equals fraction numerator begin display style 1 end style over denominator begin display style 2 cross times 2 cross times 2 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction 2 sin fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction cos open parentheses fraction numerator begin display style 4 straight pi end style over denominator begin display style 14 end style end fraction close parentheses equals fraction numerator begin display style 1 end style over denominator begin display style 8 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction sin fraction numerator 8 straight pi over denominator 14 end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 8 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction sin open parentheses straight pi minus fraction numerator begin display style 8 straight pi end style over denominator begin display style 14 end style end fraction close parentheses equals fraction numerator begin display style 1 end style over denominator begin display style 8 cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style end fraction sin fraction numerator 6 straight pi over denominator 14 end fraction equals 1 over 8 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space sin fraction numerator begin display style 6 straight pi end style over denominator begin display style 14 end style end fraction equals cos fraction numerator begin display style straight pi end style over denominator 14 end fraction end style
Answered by Expert 9th July 2018, 1:58 PM
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