JEE Math Practice Question
Let f : R $$\to$$ R be defined as $$f(x + y) + f(x - y) = 2f(x)f(y),f\left( {{1 \over 2}} \right) = - 1$$. Then, the value of $$\sum\limits_{k = 1}^{20} {{1 \over {\sin (k)\sin (k + f(k))}}} $$ is equal to :
- A.cosec2(21) cos(20) cos(2)
- B.sec2(1) sec(21) cos(20)
- C.cosec2(1) cosec(21) sin(20)
- D.sec2(21) sin(20) sin(2)
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