Question

y=3sint -sin³t
X
=3cost -cos³t
Find dy/dx
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Answer 1

$y = 3sint - {sin}^{3} t \\ x = 3cos - {cos}^{3} t \\ \frac{dy}{dt} = 3cost - 3 {sin}^{2}t .cost \\ \frac{dx}{dt} = - 3sint + 3 {cos}^{2} t.sint \\ \frac{dy}{dx } = \frac{dy}{dt} \times \frac{dt}{dx} \\ \: \: = \frac{3 \cos(t) - 3 { \sin(t) }^{2}. \cos(t) }{3 { \cos}^{2} t.sint - 3sint} \\ = \frac{ \cos(t) {cos}^{2} t}{ \sin(t) ( - {sin}^{2} t)} = - { cot}^{3}t$