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  4. The number of solutions of the equation 2 θ- cos 2 θ+√2=0 is R is equal to

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

JEE MainJEE Main 2022Trigonometric Functions

Solution:

$2 \theta-\cos ^{2} \theta+\sqrt{2}=0$
$\Rightarrow \cos ^{2} \theta=2 \theta+\sqrt{2}$
$y=2 \theta+\sqrt{2}$
image
Both graphs intersect at one point.