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The distance between the points (a cos ...

The distance between the points (`a cos alpha, a sin alpha`) and (`a cos beta, a sin beta`) is

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The correct Answer is:
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`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 alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

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    B
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  • If sin beta is the G.M between sin alpha and cos alpha , then cos 2 beta is

    A
    `2 sin ^2 ((pi )/(4) - alpha)`
    B
    `2 cos^2 ((pi)/(4) - alpha)`
    C
    `2 cos^2 ((pi)/(2)+alpha )`
    D
    `2 sin ^2 (( pi)/(2 ) + alpha )`

  • If tan alpha and tan beta are the roots of x^(2) + ax + b = 0, then (sin (alpha + beta))/(sin alpha sin beta) is equal to

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