MCQ
The equation ${\sec ^2}\theta = \frac{{4xy}}{{{{(x + y)}^2}}}$ is only possible when
  • $x = y$
  • B
    $x < y$
  • C
    $x > y$
  • D
    None of these

Answer

Correct option: A.
$x = y$
a
(a) Since ${\cos ^2}\theta \le 1$

${\sec ^2}\theta = \frac{{4xy}}{{{{(x + y)}^2}}} \ge 1 $

$\Rightarrow 4xy \ge {(x + y)^2} $

$\Rightarrow {(x - y)^2} \le 0$

It is possible only when $x = y$, .$(x,\,y \in R)$

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