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CBSE Class 12-science Answered

If x = a(cos thita + thita sin thita) and y = a(sin thita – thita cos thita), show that d2y/dx2 = 1/a (sec3thita / thita) Explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:15: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x equals straight a left parenthesis cosθ plus θsinθ right parenthesis
dx over dθ equals straight a open parentheses negative sinθ plus θcosθ plus sinθ close parentheses
dx over dθ equals aθcosθ......... left parenthesis straight i right parenthesis
straight y equals straight a open parentheses sinθ minus θcosθ close parentheses
dy over dθ equals straight a open square brackets cosθ minus open parentheses negative θsinθ plus cosθ close parentheses close square brackets
dy over dθ equals straight a open square brackets cosθ plus θsinθ minus cosθ close square brackets
dy over dθ equals aθsinθ........ left parenthesis ii right parenthesis
dy over dx equals aθsinθ over aθcosθ
dy over dx equals tanθ
fraction numerator straight d squared straight y over denominator dx squared end fraction equals sec squared straight theta dθ over dx
fraction numerator straight d squared straight y over denominator dx squared end fraction equals sec squared straight theta cross times 1 over aθcosθ
fraction numerator straight d squared straight y over denominator dx squared end fraction equals fraction numerator sec cubed straight theta over denominator aθ end fraction
end style
Answered by Sneha shidid | 28 Aug, 2018, 12:05: PM
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Differentiate space straight y equals square root of fraction numerator straight x squared plus 2 over denominator straight x squared plus 3 end fraction end root 
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