Đáp án:
$\begin{array}{l}
a){\cos ^2}{15^0} + {\cos ^2}{25^0} + {\cos ^2}{35^0} + {\cos ^2}{45^0}\\
+ {\cos ^2}{55^0} + {\cos ^2}{65^0} + {\cos ^2}{75^0}\\
= \left( {{{\cos }^2}{{15}^0} + {{\cos }^2}{{75}^0}} \right) + \left( {{{\cos }^2}{{25}^0} + {{\cos }^2}{{65}^0}} \right)\\
+ \left( {{{\cos }^2}{{35}^0} + {{\cos }^2}{{55}^0}} \right) + {\cos ^2}{45^0}\\
= \left( {{{\cos }^2}{{15}^0} + {{\sin }^2}{{15}^0}} \right) + \left( {{{\cos }^2}{{25}^0} + {{\sin }^2}{{25}^0}} \right)\\
+ \left( {{{\cos }^2}{{35}^0} + {{\sin }^2}{{35}^0}} \right) + {\left( {\frac{1}{{\sqrt 2 }}} \right)^2}\\
= 1 + 1 + 1 + \frac{1}{2} = \frac{7}{2}\\
b){\sin ^2}{10^0} - {\sin ^2}{20^0} + {\sin ^2}{30^0} - {\sin ^2}{40^0}\\
- {\sin ^2}{50^0} - {\sin ^2}{70^0} + {\sin ^2}{80^0}\\
= \left( {{{\sin }^2}{{10}^0} + {{\sin }^2}{{80}^0}} \right) - \left( {{{\sin }^2}{{20}^0} + {{\sin }^2}{{70}^0}} \right)\\
- \left( {{{\sin }^2}{{40}^0} + {{\sin }^2}{{50}^0}} \right) + {\sin ^2}{30^0}\\
= 1 - 1 - 1 + {\left( {\frac{1}{2}} \right)^2} = - 1 + \frac{1}{4} = - \frac{3}{4}\\
c)\sin {15^0} + \sin {75^0} - \cos {15^0} - \cos {75^0} + \sin {30^0}\\
= \sin {30^0}\\
= \frac{1}{2}\\
d)\sin {35^0} + \sin {67^0} - \cos {23^0} - \cos {55^0}\\
= 0\\
e){\cos ^2}{20^0} + {\cos ^2}{40^0} + {\cos ^2}{50^0} + {\cos ^2}{70^0}\\
= 2\\
f)\sin {20^0} - \tan {40^0} + \cot {50^0} - \cos {70^0}\\
= 0
\end{array}$
