If x cos ⁡α+y sin ⁡α=x cos ⁡β+y sin⁡ β=2a, then cos ⁡α cos ⁡β is,

If x cos α+y sin α=x cos β+y sin β=2athen cos α cos β is,

  1. A

    4axx2+y2

  2. B

    4a2y2x2+y2

  3. C

    4ayx2+y2

  4. D

    4a2x2x2+y2

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    Solution:

    We have,

    xcosα+ysinα=xcosβ+ysinβ=2a

     α,β are the roots of x cosθ+y sinθ=2a

    Now, 

    xcosθ+ysinθ=2a(xcosθ2a)2=y2sin2θx2cos2θ4axcosθ+4a2=y21cos2θx2+y2cos2θ4axcosθ+4a2y2=0

    Clearly, cos α,cos β are the roots of this equation. 

     cosαcosβ=4a2y2x2+y2.

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