Giá trị của

\(M = {\cos ^2}15 + {\cos ^2}25 + {\cos ^2}35 + {\cos ^2}45 + {\cos ^2}105 + {\cos ^2}115 + {\cos ^2}125\)là ?

\(M = {\cos ^2}15 + {\cos ^2}25 + {\cos ^2}35 + {\cos ^2}45 + {\cos ^2}105 + {\cos ^2}115 + {\cos ^2}125\)

\( = {\cos ^2}15 + {\cos ^2}25 + {\cos ^2}35 + {\cos ^2}45 + {\sin ^2}15 + {\sin ^2} + {\sin ^2}25 + {\sin ^2}35\)

\( = \left( {{{\cos }^2}15 + {{\sin }^2}15} \right)\left( {{{\sin }^2}25 + {{\cos }^2}25} \right) + \left( {{{\cos }^2}35 + {{\sin }^2}35} \right) + {\cos ^2}45\)

= 1 + 1 + 1 + \(\frac{1}{2} = \frac{7}{2}\).