Question

The number of solutions of the equation $2\theta -{\cos }^2\theta +\sqrt{2}=0$ is $R$ is equal to ____

Answer 1

Answer: 1

$2\theta -{\cos }^2\theta +\sqrt{2}=0$
$\Rightarrow {\cos }^2\theta =2\theta +\sqrt{2}$
$y=2\theta +\sqrt{2}$

Both graphs intersect at one point.