If $\tan x = \frac{{2b}}{{a - c}}(a \ne c),$

$y = a\,{\cos ^2}x + 2b\,\sin x\cos x + c\,{\sin ^2}x$

and $z = a{\sin ^2}x - 2b\sin x\cos x + c{\cos ^2}x,$ then

  • A

    $y = z$

  • B

    $y + z = a + c$

  • C

    $y - z = a + c$

  • D

    $y - z = {(a - c)^2} + 4{b^2}$

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  • [IIT 1964]

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