Sir/Mam,please explain the answer of question no.33

Asked by bhuwnesh16 | 24th Apr, 2017, 04:34: PM

Expert Answer:

begin mathsize 16px style limit as alpha rightwards arrow beta of fraction numerator sin squared alpha minus sin squared beta over denominator alpha squared minus beta squared end fraction
limit as alpha rightwards arrow beta of fraction numerator begin display style open parentheses sin alpha plus sin beta close parentheses open parentheses sin alpha minus sin beta close parentheses end style over denominator begin display style open parentheses alpha plus beta close parentheses open parentheses alpha minus beta close parentheses end style end fraction
limit as alpha rightwards arrow beta of fraction numerator begin display style 2 sin open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses 2 cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses sin open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end style over denominator begin display style open parentheses alpha plus beta close parentheses open parentheses alpha minus beta close parentheses end style end fraction
limit as alpha rightwards arrow beta of fraction numerator 4 sin open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses sin open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses over denominator open parentheses alpha plus beta close parentheses open parentheses alpha minus beta close parentheses end fraction

limit as alpha rightwards arrow beta of fraction numerator begin display style 4 sin open parentheses fraction numerator begin display style alpha plus beta end style over denominator begin display style 2 end style end fraction close parentheses cos open parentheses fraction numerator begin display style alpha minus beta end style over denominator begin display style 2 end style end fraction close parentheses cos open parentheses fraction numerator begin display style alpha plus beta end style over denominator begin display style 2 end style end fraction close parentheses end style over denominator begin display style open parentheses alpha plus beta close parentheses end style end fraction cross times fraction numerator begin display style sin open parentheses fraction numerator begin display style alpha minus beta end style over denominator begin display style 2 end style end fraction close parentheses end style over denominator begin display style fraction numerator alpha minus beta over denominator 2 end fraction end style end fraction cross times 1 half
fraction numerator begin display style 4 sin open parentheses fraction numerator begin display style beta plus beta end style over denominator begin display style 2 end style end fraction close parentheses cos open parentheses fraction numerator begin display style beta minus beta end style over denominator begin display style 2 end style end fraction close parentheses cos open parentheses fraction numerator begin display style beta plus beta end style over denominator begin display style 2 end style end fraction close parentheses end style over denominator begin display style open parentheses beta plus beta close parentheses end style end fraction cross times 1 cross times 1 half
fraction numerator begin display style 4 sin space beta space cos space 0 space cos space beta end style over denominator 2 beta end fraction cross times fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction
fraction numerator 2 sin space beta space cos space beta over denominator 2 beta end fraction
fraction numerator sin begin display style space end style begin display style 2 end style begin display style beta end style over denominator 2 beta end fraction

end style

Answered by Sneha shidid | 25th Apr, 2017, 08:08: AM