JEE Main 202127 Jul, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002Let f : R →\to→ R be defined as f(x+y)+f(x−y)=2f(x)f(y),f(12)=−1f(x + y) + f(x - y) = 2f(x)f(y),f\left( {{1 \over 2}} \right) = - 1f(x+y)+f(x−y)=2f(x)f(y),f(21)=−1. Then, the value of ∑k=1201sin(k)sin(k+f(k))\sum\limits_{k = 1}^{20} {{1 \over {\sin (k)\sin (k + f(k))}}}k=1∑20sin(k)sin(k+f(k))1 is equal to :AOption A. cosec²(21) cos(20) cos(2)BOption B. sec²(1) sec(21) cos(20)COption C. cosec²(1) cosec(21) sin(20)DOption D. sec²(21) sin(20) sin(2)CheckSkip · show solution
