Đáp án:
$\begin{array}{l}
Do:\sin a = \cos \left( {{{90}^0} - a} \right)\\
{\sin ^2}a + {\cos ^2}a = 1\\
a)M = {\sin ^2}{10^0} + {\sin ^2}{20^0} + {\sin ^2}{45^0}\\
+ {\sin ^2}{70^0} + {\sin ^2}{80^0}\\
= {\sin ^2}{10^0} + {\sin ^2}{20^0} + \dfrac{1}{2} + {\cos ^2}{20^0} + {\cos ^2}{10^0}\\
= 1 + 1 + \dfrac{1}{2}\\
= \dfrac{5}{2}\\
b)N = \tan {35^0}.\tan {40^0}.\tan {45^0}.\tan {50^0}.\tan {55^0}\\
= \tan {35^0}.\tan {40^0}.1.\cot {40^0}.\cot {35^0}\\
= \left( {\tan {{35}^0}.\cot {{35}^0}} \right).\left( {\tan {{40}^0}.\cot {{40}^0}} \right).1\\
= 1\\
c)\\
P = {\sin ^2}{42^0} + {\sin ^2}{43^0} + {\sin ^2}{44^0} + {\sin ^2}{45^0}\\
+ {\sin ^2}{46^0} + {\sin ^2}{47^0} + {\sin ^2}{48^0}\\
= 1 + 1 + 1 + {\sin ^2}{45^0}\\
= 3 + \dfrac{1}{2}\\
= \dfrac{7}{2}\\
Q = {\cos ^2}{15^0} - {\cos ^2}{25^0} + {\cos ^2}{35^0} - {\cos ^2}{45^0}\\
+ {\cos ^2}{55^0} - {\cos ^2}{65^0} + {\cos ^2}{75^0}\\
= {\cos ^2}{15^0} + {\cos ^2}{75^0} + {\cos ^2}{35^0} + {\cos ^2}{55^0}\\
- \left( {{{\cos }^2}{{25}^0} + {{\cos }^2}{{65}^0}} \right) - \left( {{{\cos }^2}{{45}^0}} \right)\\
= 1 + 1 - 1 - \dfrac{1}{2}\\
= \dfrac{1}{2}
\end{array}$
