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Let \(f: R \rightarrow R\) be defined as \(f(x+y)+f(x-y)=2 f(x) f(y), f\left(\frac{1}{2}\right)=-1\). Then, the value of…

Q1

Let \(f: R \rightarrow R\) be defined as \(f(x+y)+f(x-y)=2 f(x) f(y), f\left(\frac{1}{2}\right)=-1\). Then, the value of \(\sum_{k=1}^{20} \frac{1}{\sin (k) \sin (k+f(k))}\) is equal to:

[JEE Main 2021, 27 Jul (Shift 2)]

a

\(\operatorname{cosec}^2(21) \cos (20) \cos (2)\)

b

\(\sec ^2(1) \sec (21) \cos (20)\)

c

\(\sec ^2(21) \sin (20) \sin (2)\)

d

\(\operatorname{cosec}^2(1) \operatorname{cosec}(21) \sin (20)\)

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