The value of $\cos {\pi \over {{2^2}}}.\cos {\pi \over {{2^3}}}\,.....\cos {\pi \over {{2^{10}}}}.\sin {\pi \over {{2^{10}}}}$ is -

Question

${1 \over {256}}$

${1 \over {2}}$

${1 \over {1024}}$

${1 \over {512}}$

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