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If x = a cos^(3) theta, y = a sin ^(3) t...

If x = `a cos^(3) theta, y = a sin ^(3) theta then sqrt(1+((dy)/(dx))^(2))`=?

A

` tan^2 theta `

B

` sec^2 theta `

C

` sec theta `

D

` | sec theta |`

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • If x =cos^2 theta and y = sin^3 theta , then 1+((dy)/(dx))^(2) is equal to

    A
    `tan^ 2theta`
    B
    `cot^ 2theta`
    C
    `sec^(2) theta`
    D
    `"cosec"^2 theta`

  • If x=a cos^3theta,y=asin^3theta , then 1+((dy)/(dx))^2 is ___

    A
    `sec ^2 theta`
    B
    `tan theta`
    C
    1
    D
    `tan^2 theta`

  • if x=a cos^(4) theta, y= a sin^(4) theta, "then" (dy)/(dx)"at" theta=(3pi)/(4) is

    A
    `-1`
    B
    1
    C
    `-a^(2)`
    D
    `a^(2)`

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    If x=3cos theta-2cos^(3)theta,y=3sin theta-2sin^(3)theta, then (dy)/(dx) is

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    If y=log(1+ theta), x= sin^(-1) theta , then (dy)/(dx) =

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