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If x = a sin theta + b cos theta, y = a ...

If `x = a sin theta + b cos theta, y = a cos theta - b sin theta,` then show that `(ax+by)^2 +(bx - ay)^2 = (a^2+b^2)^2`

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Knowledge Check

  • If a tan theta = b, then a cos 2 theta+ b sin 2 theta =

    A
    a
    B
    b
    C
    `-a`
    D
    `-b`

  • If x= a sin 2theta (1+ cos 2theta) , y= b cos 2theta(1- cos 2theta) , then (dy)/(dx) =

    A
    `(b tan theta)/a`
    B
    `(a tan theta)/b`
    C
    `a/(b tan theta)`
    D
    `b/(a tan theta)`

  • If x = a cos theta - b sin theta and y = b cos theta + a sin theta , then the value of x^(2) + y^(2) is

    A
    `a^2`
    B
    `b^2`
    C
    `(a^2)/(b^2)`
    D
    `a^2 + b^2`

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    If x= a sin 2theta (1+ cos 2theta) , y= b cos 2theta(1- cos 2theta) , then (dy)/(dx) =

    If x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove that " x^(2)+y^(2)=a^(2)+b^(2).

    If x = a cos theta - b sin theta and y = a sin theta + b cos theta, prove that x^2 + y^2 = a^2 + b^2.

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    If tan theta = b//a , then b cos 2 theta + a sin 2 theta =

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