Question

If x = acos³t and y =asin³t, then dy/dx​

Answer 1

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given,

x = a sin^3 t

differentiate w.r.t t

dx/dt = 3 a sin^2 t . d/dx (sint)

dx/dt = 3a sin^2 t cos t………..…(A)

y= a cos ^3 t

differentiate w.r.t t

dy/dt= 3a cos ^2 t . d/dx (cos t)

dy/dt = 3a cos ^2 t(-sint)

dy/dt = - 3a cos^2 t sint ………….(B)

as we have to find,

dy/ dx = (dy /dt )/ (dx/dt)

dy/dx= -3a cos ^2t sint /3a sin^2 t. cos t

dy/dx = - cos t/sin t

dy /dx = - cot t

Answer 2

Answer:

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