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If y=1-costheta,x=1-sintheta,"then "(dy)...

If `y=1-costheta,x=1-sintheta,"then "(dy)/(dx)" at "theta=(pi)/(4)" is"`

A

`-1`

B

1

C

`(1)/(2)`

D

`(1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=1-cos theta rArr (dy)/(d theta)=sin theta,`
`x=1-sin theta rArr (dx)/(d theta)=-cos theta`
`therefore" "(dy)/(dx)=- tan theta`
`" "theta=(pi)/(4)`
`therefore" "[(dy)/(dx)]_(theta=(pi)/(4))=-tan.(pi)/(4)=-1`
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Knowledge Check

  • If y=1- cos theta, x =1 - sin theta,then (dy)/(dx) " at " theta = (pi)/(4) is

    A
    ` -1`
    B
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    C
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    `(pi)/(4)`
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    `(2)/(pi)`
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    `(pi)/(2)`

  • If x=costheta(1+costheta),y=sintheta(1+costheta)," then "((dy)/(dx))" at "theta=(pi)/(2) is

    A
    `-1`
    B
    0
    C
    1
    D
    2

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