JEE Advance - Mathematics (1984 - No. 12)
$$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)$$ is equal to
$${1 \over 2}$$
$$\cos {\pi \over 8}$$
$${1 \over 8}$$
$${{1 + \sqrt 2 } \over {2\sqrt 2 }}$$