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Continuity And Differentiability

Question
CBSEENMA12035021

Find space dy over dx when space straight x equals straight a space secө comma space straight y equals straight b space tanө space

Solution
space space space space space space space space space space space space space space straight x equals straight a space secө comma space space straight y equals straight b space tanө space
therefore space space straight b dx over dθ equals straight a space secθ space tanθ comma space dy over dθ equals straight b space sec squared
Now space dy over dx equals fraction numerator begin display style dy over dθ end style over denominator begin display style dx over dθ end style end fraction equals fraction numerator straight b space sec squared over denominator straight a space secθ space tanθ end fraction equals fraction numerator straight b space secθ over denominator straight a space tan space straight theta end fraction
equals straight b over straight a fraction numerator begin display style 1 over cosθ end style over denominator begin display style fraction numerator sin space straight theta over denominator cos space straight theta end fraction end style end fraction equals straight b over straight a fraction numerator 1 over denominator cos space straight theta end fraction cross times fraction numerator cos space straight theta over denominator sin space straight theta end fraction equals straight b over straight a fraction numerator 1 over denominator sin space straight theta end fraction equals straight b over straight a cosec space straight theta

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