Question

化简：cos21°+cos22°+cos23°+…+cos289°

化简：cos21°+cos22°+cos23°+…+cos289°．

Answer 1

cos²1°+cos²2°+cos²3°+…+cos²89°
=cos²1°+cos²89°+…+cos²44°+cos²46°+cos²45°
=（cos²1°+cos²89°）+…+（cos²44°+cos²46°）+（

2

2

）²
=

1+1+…+1

44个1

+

1

2

=44

1

2

．