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The range of the function \(f\left(x\right)={\log }_{\sqrt{5}}\left(3+\cos \left(\frac{3\pi }{4}+x\right)\right.+\cos \l…

Q1

The range of the function
\(f\left(x\right)={\log }_{\sqrt{5}}\left(3+\cos \left(\frac{3\pi }{4}+x\right)\right.+\cos \left(\frac{\pi }{4}+x\right)\left.+\cos \left(\frac{\pi }{4}-x\right)-\cos \left(\frac{3\pi }{4}-x\right)\right)\)

[JEE Main 2021, 1 Sep (Shift 2)]

a

\([-2,2]\)

b

\(\left[\frac{1}{\sqrt{5}},\sqrt{5}\right]\)

c

\((0,\sqrt{5})\)

d

\([0,2]\)

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