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CBSE Class 11-science Answered

If x=2 ln cot t and y=tan t + cot t, find dy/dx.
Asked by dineshchem108 | 10 Aug, 2018, 09:23: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x equals 2 log open parentheses cott close parentheses dx over dt equals 2 over cott cross times negative cosec squared straight t dx over dt equals fraction numerator negative 2 sint over denominator cost end fraction cross times fraction numerator 1 over denominator sin squared straight t end fraction dx over dt equals fraction numerator negative 2 over denominator sint space cost end fraction straight y equals tant plus cott dy over dt equals sec squared straight t minus cosec squared straight t dy over dt equals fraction numerator 1 over denominator cos squared straight t end fraction minus fraction numerator 1 over denominator sin squared straight t end fraction dy over dt equals fraction numerator sin squared straight t minus cos squared straight t over denominator sin squared straight t space cos squared straight t end fraction rightwards double arrow fraction numerator begin display style dy over dt end style over denominator dx over dt end fraction equals fraction numerator fraction numerator sin squared straight t minus cos squared straight t over denominator sin squared straight t space cos squared straight t end fraction over denominator fraction numerator negative 2 over denominator sint space cost end fraction end fraction rightwards double arrow dy over dx equals fraction numerator sin squared straight t minus cos squared straight t over denominator sin squared straight t space cos squared straight t end fraction cross times fraction numerator sint space cost over denominator negative 2 end fraction rightwards double arrow dy over dx equals fraction numerator sin squared straight t minus cos squared straight t over denominator negative 2 sint space cost end fraction rightwards double arrow dy over dx equals fraction numerator negative open parentheses cos squared straight t minus sin squared straight t close parentheses over denominator negative sin 2 straight t end fraction rightwards double arrow dy over dx equals fraction numerator cos 2 straight t over denominator sin 2 straight t end fraction equals tan 2 straight t end style
Answered by Sneha shidid | 13 Aug, 2018, 10:42: AM

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