Hãy tính ​\( A = {\sin ^2}{10^ \circ } + {\sin ^2}{20^ \circ } + ... + {\sin ^2}{70^ \circ }\: + {\sin ^2}{80^ \circ }\)

* Hướng dẫn giải

 \(\begin{array}{l} A = si{n^2}{10^0} + si{n^2}{20^0} + si{n^2}{30^0} + ... + si{n^2}{80^0}\\ = (si{n^2}{10^0} + si{n^2}{80^0}) + (si{n^2}{20^0} + si{n^2}{70^0}) + (si{n^2}{30^0} + si{n^2}{60^0}) + (si{n^2}{40^0} + si{n^2}{50^0})\\ = (si{n^2}{10^0} + {\cos ^2}{10^0}) + (si{n^2}{20^0} + {\cos ^2}{20^0}) + (si{n^2}{30^0} + {\cos ^2}{30^0}) + (si{n^2}{40^0} + {\cos ^2}{40^0})\\ = 1 + 1 + 1 + 1 = 4 \end{array}\)