a) \(\cos {{22\pi } \over 3} = \cos (8\pi - {{2\pi } \over 3})\)
\(= \cos ( - {{2\pi } \over 3}) = \cos ({{2\pi } \over 3}) \)
\(= - \cos {\pi \over 3} = {{ - 1} \over 2}\)
b) \(\sin {{23\pi } \over 4} = \sin (6\pi - {\pi \over 4})\)
\(= \sin ( - {\pi \over 4}) = - \sin ({\pi \over 4}) = - {{\sqrt 2 } \over 2}\)
\(\eqalign{c) \, \, & \sin {{25\pi } \over 3} - \tan {{10\pi } \over 3} \cr&= \sin (8\pi + {\pi \over 3}) - \tan (3\pi + {\pi \over 3}) \cr & = sin{\pi \over 3} - \tan {\pi \over 3} = {{\sqrt 3 } \over 2} - \sqrt 3 \cr&= {{ - \sqrt 3 } \over 2} \cr} \)
d) \({\cos ^2}{\pi \over 8} - {\sin ^2}{\pi \over 8} = \cos {\pi \over 4} = {{\sqrt 2 } \over 2}.\)
