Question

$\sin \Theta =\frac{1}{2}(\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}})$ necessarily $implies$

• A. $x>y$
• B. $x<y$
• C. $x=y$
• D. both $x$ and $y$ are purely imaginary

Answer 1

Answer: (C)

$x=y$

using AM-GM inequality
$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}\ge 2$
$\therefore 2\sin x\ge 2$
holds only when $\sin x=1$
that is $x=y$