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Find the distance between the points P(a...

Find the distance between the points `P(asinalpha, acosalpha)` and `Q(a cos alpha,-a sinalpha)`

Text Solution

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The correct Answer is:
NA
`PQ=sqrt(a^2(cosalpha-cosbeta)^2=a^2(sinalpha-beta)^2)`
`a=sqrt(sin^2alpha+cos^2alpha+cos^2beta+sin^2beta-2cosalphacosbeta-2sinalphasinbeta)`
`a=sqrt(2(1-cos(alpha-beta))`
`a=sqrt(2xx2sin^(2).(alpha-beta)/(2))`
`=2a"sin"(alpha-beta)/(2)`
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Knowledge Check

  • If tantheta=(sin alpha-cos alpha)/(sinalpha+cosalpha)1 then

    A
    `sinalpha-cosalpha=+-sqrt2sintheta`
    B
    `sinalpha+cosalpha=+-sqrt2costheta`
    C
    `cos2theta-sin2alpha`
    D
    `sin2theta+cos2alpha=0`

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