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The area of the region \(A=\left{(x,y):\left|\cos x−\sin x\right|\leq y\leq \sin x,0\leq x\leq \frac{\pi }{2}\right}\) i…

Q1

The area of the region \(A=\left{(x,y):\left|\cos x−\sin x\right|\leq y\leq \sin x,0\leq x\leq \frac{\pi }{2}\right}\) is

[JEE Main 2023, 29 Jan (Shift 2)]

a

\(1−\frac{3}{\sqrt{2}}+\frac{4}{\sqrt{5}}\)

b

\(\sqrt{5}+2\sqrt{2}−4.5\)

c

\(\frac{3}{\sqrt{5}}−\frac{3}{\sqrt{2}}+1\)

d

\(\sqrt{5}−2\sqrt{2}+1\)

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