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CBSE Class 12-science Answered

If x = a( cos thita + log tan thita/2)  and y = a sin thita,   show that the value of d2y/dx2 at thita = pie/4 is 4/a Explain in great detail    
Asked by haroonrashidgkp | 25 Aug, 2018, 07:07: PM
answered-by-expert Expert Answer
begin mathsize 18px style straight x space equals straight a space open parentheses cos space straight theta space plus space log space open parentheses tan space open parentheses straight theta over 2 close parentheses space close parentheses close parentheses fraction numerator dx over denominator straight d straight theta end fraction equals straight a open parentheses negative sin space straight theta space plus space fraction numerator 1 over denominator tan space open parentheses straight theta over 2 close parentheses end fraction cross times sec squared space open parentheses straight theta over 2 close parentheses space cross times 1 half close parentheses fraction numerator dx over denominator straight d straight theta end fraction equals negative sin space straight theta space plus fraction numerator 1 over denominator 2 space sin space open parentheses straight theta over 2 close parentheses space cos space open parentheses straight theta over 2 close parentheses end fraction equals negative sin space straight theta space plus fraction numerator 1 over denominator sin space straight theta space end fraction equals straight a open parentheses fraction numerator cos squared straight theta over denominator sin space straight theta end fraction close parentheses straight y equals space sint dy over dt equals straight a space cos space straight t dy over dx equals fraction numerator dy over denominator straight d straight theta end fraction cross times fraction numerator straight d straight theta over denominator dx end fraction equals straight a space cos space straight theta cross times fraction numerator sin space straight theta over denominator cos squared straight theta end fraction equals space tan space straight theta fraction numerator straight d squared straight y over denominator dx squared end fraction equals sec squared space straight t cross times dt over dx equals sec squared space straight t cross times fraction numerator sin space straight t over denominator straight a space cos squared straight t end fraction fraction numerator straight d squared straight y over denominator dx squared end fraction equals open parentheses square root of 2 close parentheses squared cross times fraction numerator begin display style fraction numerator 1 over denominator square root of 2 end fraction end style over denominator begin display style 1 half end style end fraction equals fraction numerator 4 over denominator straight a square root of 2 end fraction end style
Answered by Arun | 28 Aug, 2018, 11:23: AM

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