Question

求sin²1°+sin²2°+sin²3°+…+sin²88°+sin²89°的值    ．

Answer

通过诱导公式sin89°=cos1°，得出sin21°+cos21°=1，依此类推，得出原式=44×1+sin245°，得出答案．
【解析】
∵sin89°=cos（90°-1°）=cos1°
∴sin21°+sin289°=sin21°+cos21°=1
同理sin2°+sin88°=1，…sin44°+sin46°=1
∴sin21°+sin22°+sin23°+…+sin288°+sin289°=44+=44.5
故答案为44.5．