JEE Advance - Mathematics (1994 - No. 18)
If $$\omega \,$$ is an imaginary cube root of unity then the value of $$\sin \left\{ {\left( {{\omega ^{10}} + {\omega ^{23}}} \right)\pi - {\pi \over 4}} \right\}$$ is
$$ - {{\sqrt 3 } \over 2}\,$$
$$ - {1 \over {\sqrt 2 }}$$
$${1 \over {\sqrt 2 }}$$
$${{\sqrt 3 } \over 2}$$