Question

sin1°^2 sin2°^2 sin3°^2 ... sin89°^2

把步骤写明白，谢谢啦

Answer 1

sin1°^2+ sin2°^2 +sin3°^2+ ... +sin87°^2+sin88°^2+sin89°^2
=sin1°^2+ sin2°^2 +sin3°^2+ ... +sin(90°-3°)^2+sin(90°-2°)^2+sin(90°-1°)^2
=sin1°^2+ sin2°^2 +sin3°^2+ ... +cos3°^2+cos1°^2+cos1°^2
=sin1°^2+cos1°^2+sin2°^2+cos2°^2+sin3°^2+cos3°^2+............+sin45°^2
=1+1+1+............+(√2/2)^2 除掉sin45°^2,共89-1=88个，以两个为1组，共88/2=44组
=44+1/2
=89/2

Answer 2

应该是
sin²1°+ sin²2° +sin²3°+ ...+ sin²89°
=sin²1°+sin²2°+sin²3°+……+sin²44°+sin²45°+cos²44°…+cos²2+cos²1°
=1+1……+1+（√2/2）²
=44+1/2
=44又1/2

Answer 3

最简单的写法为:(首项 尾项)×项数÷2
即:[sin^2(1°) sin^2(89°)]×89×1/2=44.5

Answer 4

加还是乘？

Answer 5

？