sin1°+sin2°+sin3°+···+sin88°+sin89°+sin90°
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S = sin1°+sin2°+sin3°+···+sin88°+sin89°+sin90°
两边乘 2sin(1/2), 并且用公式 2sin x sin y = cos(x-y) - cos(x+y)
2sin(1/2) S
= [cos(1/2) - cos(3/2)] + [cos(3/2) - cos(5/2)] + ... + [cos(179/2) - cos(181/2)]
= cos(1/2) - cos(181/2)
= cos(1/2) + sin(1/2)
S = (1/2)[cot(1/2) + 1]
两边乘 2sin(1/2), 并且用公式 2sin x sin y = cos(x-y) - cos(x+y)
2sin(1/2) S
= [cos(1/2) - cos(3/2)] + [cos(3/2) - cos(5/2)] + ... + [cos(179/2) - cos(181/2)]
= cos(1/2) - cos(181/2)
= cos(1/2) + sin(1/2)
S = (1/2)[cot(1/2) + 1]
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sin1°=cos89°,(sina)^2+(cosa)^2=1,
sin1°+sin2°+sin3°+···+sin88°+sin89°+sin90°
=44+1/2+1=45.5
sin1°+sin2°+sin3°+···+sin88°+sin89°+sin90°
=44+1/2+1=45.5
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