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Home / Doubts and Solutions/JEE/Mathematics

Prove that

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Asked by Anish 11th July 2018, 1:35 PM
Answered by Expert
Answer:
begin mathsize 16px style fraction numerator cos space 3 straight alpha plus cos space 3 straight beta over denominator 2 cos open parentheses straight alpha minus straight beta close parentheses minus 1 end fraction LHS equals fraction numerator 2 cos space 3 open parentheses begin display style fraction numerator straight alpha plus straight beta over denominator 2 end fraction end style close parentheses cos space 3 open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses over denominator 2 open parentheses 2 cos open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses minus 1 close parentheses minus 1 end fraction space now comma cos space 3 open parentheses fraction numerator begin display style straight alpha minus straight beta end style over denominator begin display style 2 end style end fraction close parentheses equals 4 cos cubed open parentheses fraction numerator begin display style straight alpha minus straight beta end style over denominator begin display style 2 end style end fraction close parentheses minus 3 space cos space open parentheses fraction numerator begin display style straight alpha minus straight beta end style over denominator begin display style 2 end style end fraction close parentheses LHS equals fraction numerator begin display style 2 cos space 3 open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses open parentheses 4 cos cubed open parentheses fraction numerator begin display style straight alpha minus straight beta end style over denominator begin display style 2 end style end fraction close parentheses minus 3 space cos space open parentheses fraction numerator begin display style straight alpha minus straight beta end style over denominator begin display style 2 end style end fraction close parentheses close parentheses end style over denominator 2 open parentheses 2 cos open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses minus 1 close parentheses minus 1 end fraction equals 2 cos space 3 open parentheses fraction numerator begin display style straight alpha plus straight beta end style over denominator begin display style 2 end style end fraction close parentheses cos space open parentheses fraction numerator begin display style straight alpha minus straight beta end style over denominator begin display style 2 end style end fraction close parentheses RHS space equals space cos space straight alpha space cos space open parentheses straight alpha plus straight beta close parentheses minus sin space straight alpha space sin space open parentheses straight alpha plus straight beta close parentheses equals cos space open parentheses 2 straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha plus 2 straight beta close parentheses equals 2 cos space 3 open parentheses fraction numerator begin display style straight alpha plus straight beta end style over denominator begin display style 2 end style end fraction close parentheses cos space open parentheses fraction numerator begin display style straight alpha minus straight beta end style over denominator begin display style 2 end style end fraction close parentheses end style
Answered by Expert 23rd July 2018, 11:18 AM
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