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If \(y^2+\log _e\left(\cos ^2 x\right)=y, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\),Then: [JEE Main 2020, 3 Sep …

Q1

If \(y^2+\log _e\left(\cos ^2 x\right)=y, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\),Then:

[JEE Main 2020, 3 Sep (Shift 1)]

a

\( \left|y^{\prime}(0)\right|+\left|y^{\prime \prime}(0)\right|=3 \)

b

\( \left|y^{\prime \prime}(0)\right|=2 \)

c

\( \left|y^{\prime}(0)\right|+\left|y^{\prime \prime}(0)\right|=1 \)

d

\( \left|y^{\prime \prime}(0)\right|=0 \)

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