Number of solutions of equation 2 θ-cos ^{2} θ+√{2}=0 is R is equal to

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Trigonometrical Equations

hard

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

A

$1$

B

$2$

C

$3$

D

$4$

(JEE MAIN-2022)

Solution

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

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

$y=2 \theta+\sqrt{2}$

Both graphs intersect at one point.

Standard 11

Mathematics

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