Tính S = cos ^2 5 ∘ + cos ^2 10 ∘ + cos ^2 15 ∘ + . . . + cos ^2 80 ∘ + cos^ 2 85 ∘ .
Giải thích
\(S = {\cos ^2}5^\circ + {\cos ^2}10^\circ + {\cos ^2}15^\circ + ... + {\cos ^2}80^\circ + {\cos ^2}85^\circ \)
\( = {\cos ^2}5^\circ + {\cos ^2}10^\circ + {\cos ^2}15^\circ + ... + {\sin ^2}15^\circ + {\sin ^2}10^\circ + {\sin ^2}5^\circ \)
\[ = \left( {{{\cos }^2}5^\circ + {{\sin }^2}5^\circ } \right) + \left( {{{\cos }^2}10^\circ + {{\sin }^2}10^\circ } \right) + \left( {{{\cos }^2}15^\circ + {{\sin }^2}15^\circ } \right) + ... + \left( {{{\cos }^2}40^\circ + {{\sin }^2}40^\circ } \right) + {\cos ^2}45^\circ \]
\[ = 1 + 1 + 1 + ... + 1 + {\left( {\frac{{\sqrt 2 }}{2}} \right)^2}\]
\[ = 8 + \frac{1}{2} = 8,5\].
Trả lời: 8,5.