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CBSE Class 12-science Answered

If x = cos t + log tan t/2 and y = sin t then find values of d2y/dt2 and d2y/dx2 at t = pie/4 Explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:08: PM
answered-by-expert Expert Answer
begin mathsize 18px style straight x space equals space cos space straight t space plus space log space open parentheses tan space open parentheses straight t over 2 close parentheses space close parentheses dx over dt equals negative sin space straight t space plus space fraction numerator 1 over denominator tan space open parentheses straight t over 2 close parentheses end fraction cross times sec squared space open parentheses straight t over 2 close parentheses space cross times 1 half dx over dt equals negative sin space straight t space plus fraction numerator 1 over denominator 2 space sin space open parentheses straight t over 2 close parentheses space cos space open parentheses straight t over 2 close parentheses end fraction equals negative sin space straight t space plus fraction numerator 1 over denominator sin space straight t space end fraction equals fraction numerator cos squared straight t over denominator sin space straight t end fraction straight y equals space sint dy over dt equals cos space straight t dy over dx equals dy over dt cross times dt over dx equals cos space straight t cross times fraction numerator sin space straight t over denominator cos squared straight t end fraction equals space tan space straight t 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 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 2 square root of 2 end style
Answered by Arun | 28 Aug, 2018, 11:12: AM

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CBSE 12-science - Maths
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