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If the line joining the points (a cos th...

If the line joining the points `(a cos theta , b sin theta)` and `(a cos phi, b sin phi)`.Prove that the equation of this lines is `x/a "cos" (theta + phi)/2 + y/b"sin" (theta + phi)/2 = "cos" (theta -phi)/2`

Answer

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Knowledge Check

  • The number of solutions of cos 2 theta = sin theta in (0, 2pi) is

    A
    1
    B
    2
    C
    3
    D
    4

  • int ((sin theta +cos theta ))/(sqrt(sin 2 theta)) d theta is equal to :

    A
    ` log | cos theta -sin theta + sqrt (sin 2 theta ) |+c `
    B
    ` log | sin theta -cos theta + sqrt (sin 2 theta ) |+c `
    C
    `sin ^(-1) (sin theta - cos theta) +c`
    D
    ` sin ^(-1) (sin theta + cos theta )+c`

  • The normal to the curve x = a (cos theta + theta sin theta), y = a (sin theta - theta cos theta) at any point theta

    A
    passes through the origin.
    B
    makes an angle `pi//2 + theta` with the x-axis.
    C
    passes through `(a (pi)/(2), - a)`
    D
    is at a constant distance from the origin.

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    If A=[[cos theta, sin theta],[ -sin theta, cos theta]] , then prove that A^n=[[cos ntheta, sinn theta],[ -sin n theta, cos n theta]] , n in N .

    If the coordinates of a variable point P are ( a cos theta, b sin theta ), where theta is a variable quantity, then find the locus of P.

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