Question

If $\text{cosec}\theta =\frac{x^2+y^2}{2xy}$ and $(x,y)\ne (0,0)$, then this is possible for

• A. $x=y$
• B. all $x,y\in R$
• C. all $x,y\notin R$
• D. $x=2y$

Answer 1

Answer: (B)

all $x,y\in R$

Clearly $|cosec\theta |=\frac{x^2+y^2}{2|xy|}$
Now using AM-GM inequality, we get
$x^2+y^2>2|xy|$
So this gives $cosec\theta >1$ which is true for all $x,y$