a)
$ \sin \alpha = \cos(90^o - \alpha) $
Tương tự ta các giá trị
$\begin{array}{l} {\sin ^2}{10^o} + {\sin ^2}{20^o} + {\sin ^2}{30^o} + ... + {\sin ^2}{80^o}\\ = \left( {{{\sin }^2}{{10}^o} + {{\sin }^2}{{80}^o}} \right) + \left( {{{\sin }^2}{{20}^o} + {{\sin }^2}{{70}^o}} \right) + \left( {{{\sin }^2}{{30}^o} + {{\sin }^2}{{60}^o}} \right) + \left( {{{\sin }^2}{{40}^o} + {{\sin }^2}{{50}^o}} \right)\\ = \left( {{{\cos }^2}{{80}^o} + {{\sin }^2}{{80}^o}} \right) + \left( {{{\cos }^2}{{70}^o} + {{\sin }^2}{{70}^o}} \right) + \left( {{{\cos }^2}{{60}^o} + {{\sin }^2}{{60}^o}} \right) + \left( {{{\cos }^2}{{50}^o} + {{\sin }^2}{{50}^o}} \right)\\ = 1 + 1 + 1 + 1 = 4 \end{array}$
b)
$\begin{array}{l} {\cos ^2}{12^o} + {\cos ^2}{78^o} + {\cos ^2}{1^o} + {\cos ^2}{89^o}\\ = \left( {{{\cos }^2}{1^o} + {{\cos }^2}{{89}^o}} \right) + \left( {{{\cos }^2}{{12}^o} + {{\cos }^2}{{78}^o}} \right)\\ = \left( {{{\sin }^2}{{89}^o} + {{\cos }^2}{{89}^o}} \right) + \left( {{{\sin }^2}{{78}^o} + {{\cos }^2}{{78}^o}} \right)\\ = 1 + 1 = 2 \end{array}$
