Q. $\sin^{2}\theta = \frac{4xy}{(x + y)^{2}}$ is true if and only if
A) $x + y \neq 0$
B) $x = y,\ x \neq 0,\ y \neq 0$
C) $x = y$
D) $x \neq 0,\ y \neq 0$
Explanation
(b)
We know that $\sin^{2}{\theta \geq 1}$
$\Rightarrow \ \ \frac{4xy}{(x + y)^{2}} \geq 1$
$\Rightarrow \ \ 4xy \geq (x + y)^{2}$
$\Rightarrow \ \ (x - y)^{2} \leq 0$
$\Rightarrow \ \ x - y = 0\ \ \Rightarrow \ \ y = x$
And $x \neq 0,\ \ \ y \neq 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.