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CBSE Class 12-science Answered

if x = sin3t/(cos 2t)1/2,    y = cos3t/(cos 2t)1/2 , find dy/dx 

explain in great detail

Asked by haroonrashidgkp | 24 Aug, 2018, 10:51: PM
Expert Answer
begin mathsize 16px style straight x equals fraction numerator sin cubed straight t over denominator square root of cos 2 straight t end root end fraction
dx over dt equals fraction numerator square root of cos 2 straight t end root open parentheses 3 sin squared tcost close parentheses minus sin cubed straight t cross times begin display style fraction numerator 1 over denominator 2 square root of cos 2 straight t end root end fraction end style cross times negative 2 sin 2 straight t over denominator cos 2 straight t end fraction
dx over dt equals fraction numerator square root of cos 2 straight t end root open parentheses 3 sin squared tcost close parentheses minus sin cubed straight t cross times begin display style fraction numerator 1 over denominator square root of cos 2 straight t end root end fraction end style cross times negative sin 2 straight t over denominator cos 2 straight t end fraction
dx over dt equals fraction numerator 3 cos 2 tsin squared tcost plus sin cubed tsin 2 straight t over denominator cos 2 straight t square root of cos 2 straight t end root end fraction.......... left parenthesis straight i right parenthesis
straight y equals fraction numerator cos cubed straight t over denominator square root of cos 2 straight t end root end fraction
dy over dt equals fraction numerator square root of cos 2 straight t end root open parentheses negative 3 cos squared tsint close parentheses minus cos cubed straight t cross times begin display style fraction numerator 1 over denominator 2 square root of cos 2 straight t end root end fraction end style cross times negative 2 sin 2 straight t over denominator cos 2 straight t end fraction
dy over dt equals fraction numerator negative 3 cos 2 tcos squared tsint plus cos cubed tsin 2 straight t over denominator cos 2 straight t square root of cos 2 straight t end root end fraction......... left parenthesis ii right parenthesis
Find space dy over dx equals fraction numerator begin display style dy over dt end style over denominator begin display style dx over dt end style end fraction equals negative cot space 3 straight t
end style
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