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"If "x=sint, y=tant," then "dy/dx is...

`"If "x=sint, y=tant," then "dy/dx` is

A

`cos^(3)t`

B

`1/cos^(3)t`

C

`sin^(2)t`

D

`1/sin^(2)t`

Text Solution

Verified by Experts

`"We have "x=phi(t),y=psi(t)." Therefore,"`
`(dy)/(dx)=((dy)/(dt))/((dx)/(dt))=(psi')/(phi')`
`"or "(d^(2)y)/(dx^(2))=(d)/(dx)((psi')/(phi'))=(d)/(dt)((psi')/(phi'))(dt)/(dx)`
`=(phi'psi''-psi'phi'')/(phi'^(2))(1)/(phi')=(phi'psi''-psi'phi'')/(phi'^(3))`
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