1.

If x and y are connected parametrically by the equations given, without eliminating the parameter, Find `(dy)/(dx)`.`x=(sin^3t)/(sqrt(cos2t)), y=(cos^3t)/(sqrt(cos2t))`

Answer» `y = cos^3t/sqrt(cos2t)`
`dy/dt = 1/(cos2t)(sqrt(cos2t)(3cos^2t)(-sint) - cos^3t(1/2(1/(sqrt(cos2t))(-sin2t)(2)))`
`dy/dt = 1/(cos2t)(-sqrt(cos2t)(3cos^2t)(sint) +(cos^3tsin2t)/(sqrt(cos2t)))`
`dy/dt = 1/((cos2t)(sqrt(cos2t)))(cos^3tsin2t-3cos^2tsintcos2t)->(1)`
`x = sin^3t/sqrt(cos2t)`
`dx/dt = 1/(cos2t)(sqrt(cos2t)(3sin^2t)(cost) - sin^3t(1/2(1/(sqrt(cos2t))(-sin2t)(2)))`
`dx/dt = 1/(cos2t)(sqrt(cos2t)(3sin^2t)(cost) +(sin^3tsin2t)/(sqrt(cos2t)))`
`dx/dt = 1/((cos2t)(sqrt(cos2t)))(3sin^2tcostcos2t + sin^3tsin2t)->(2)`
Dividing (1) by (2),
`dy/dx = (cos^3tsin2t-3cos^2tsintcos2t)/(3sin^2tcostcos2t + sin^3tsin2t)`


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