If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =

Question

If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =

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Amara 1 month 2021-09-22T21:15:05+00:00 1 Answer 0 views 0

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    2021-09-22T21:16:57+00:00

    Answer:

    Expand the determinant w.r.t. Its row

    Δ=cos(A−B)sin(C+A−B−C)+…+…

    =cos(A−B)sin(A−B)+…+…

    =

    2

    1

    [sin(2A−2B)+sin(2B−2C)+sin(2C−2A)]

    =

    2

    1

    (−4)sin(A−B)sin(B−C)sin(C−A),

    =−2sin(A−B)sin(B−C)sin(C−A)=0

    ⇒ either A=B or B=C or C=A

    i.e. if A,B,C be the angles of a triangle then the triangle must be isosceles.

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