Bài 5. Không dung máy tính hoặc bảng số, hãy tính: a) A= cos²20°+ cos²30°+ cos²40°+ cos²50°+ cos²60°+ cos²70° b) B= sin²5° +sin²25°+ sin²45°+ sin²65°+ sin²85°

#andy

\[\begin{array}{l}
a)A = co{s^2}{20^o} + co{s^2}{30^o} + co{s^2}{40^o} + co{s^2}{50^o} + co{s^2}{60^o} + co{s^2}{70^o}\\
 = co{s^2}{20^o} + co{s^2}{30^o} + co{s^2}{40^o} + si{n^2}{40^o} + si{n^2}{30^o} + si{n^2}{20^o}\\
 = (co{s^2}{20^o} + si{n^2}{20^o}) + (si{n^2}{30^o} + co{s^2}{30^o}) + (si{n^2}{40^o} + co{s^2}{40^o})\\
 = 1 + 1 + 1\\
 = 3\\
b)B = si{n^2}{5^o} + si{n^2}{25^o} + si{n^2}{45^o} + si{n^2}{65^o} + si{n^2}{85^o}\\
 = si{n^2}{5^o} + si{n^2}{25^o} + si{n^2}{45^o} + co{s^2}{25^o} + co{s^2}{5^o}\\
 = (si{n^2}{5^o} + co{s^2}{5^o}) + (co{s^2}{25^o} + si{n^2}{25^o}) + si{n^2}{45^o}\\
 = 1 + 1 + si{n^2}{45^o}\\
 = 2 + si{n^2}{45^o}
\end{array}\]