Question

$Find space dy over dx when space straight x space equals straight a space left parenthesis cosө plus straight ө space sinө right parenthesis comma space straight y space equals space straight a space left parenthesis sinө space minus space straight ө space cosө right parenthesis$

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Solution

space space space space space space straight x equals straight a left parenthesis cosө plus straight ө space sinө right parenthesis comma space straight y equals straight a left parenthesis sinө minus straight ө space cosө right parenthesis dx over dθ equals straight a left parenthesis negative sinθ plus straight theta space cosθ plus sinθ right parenthesis equals straight a space straight theta space cosθ dy over dθ equals straight a left parenthesis cosθ plus straight theta space sinθ minus cosθ right parenthesis equals straight a space straight theta space sinθ 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 a space straight theta space sinθ over denominator straight a space straight theta space cosθ end fraction equals tanθ

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