Question

The equation $\cos \theta =x+\frac{P}{x},x\in R$ has a real solution for
$\theta$, then

• A. $p=1$
• B. $p\ge 1$
• C. $p\le \frac{1}{4}$
• D. $p\ge \frac{1}{4}$

Answer 1

The correct option is C $p\le \frac{1}{4}$

given equation gives
$x^2-x\cos \Theta +P=0$
now $x$ is real so discriminant is $>0$
so ${\cos }^2\Theta -4P>0$
so $P<\frac{{\cos }^2\Theta }{4}<\frac{1}{4}$