Question

求sin21°+sin22°+sin23°+…+sin289°的值是（　　）A．89B．892C．45D．45

求sin21°+sin22°+sin23°+…+sin289°的值是（　　）A．89B．892C．45D．452

Answer 1

sin²1°+sin²2°+sin²3°+…+sin²89°=（sin²1°+sin²89°）+（sin²2°+sin²88°）+（sin²3°+sin²87°）+…+（sin²44°+sin²46°）+sin²45°
═（sin²1°+cos²1°）+（sin²2°+cos²2°）+（sin²3°+cos²3°）+…+（sin²44°+cos²44°）+sin²45°=44+(

2

2

)2=

89

2

，
故选：B．