sin210°+sin220°+sin230°+sin240°+sin250°+sin260°+sin270°+sin280
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sin210°+sin220°+sin230°+sin240°+sin250°+sin260°+sin270°+sin280
sin210°+sin220°+sin230°+sin240°+sin250°+sin260°+sin270°+sin280
sin210°+sin220°+sin230°+sin240°+sin250°+sin260°+sin270°+sin280
利用和差化积公式:
sin(α) + sin(β) = 2sin[(α+β)/2] cos((α-β)/2)
cos(α) + cos(β) = 2cos[(α+β)/2] cos((α-β)/2)
原式每两项利用和差化积公式:
=2cos5° [ sin215° + sin235° + sin255° + sin275°)
=4cos5°cos10° [ sin225° + sin265° ]
=8cos5°cos10°cos20°sin245°
=8cos5°cos10°cos20°sin245° sin5°/sin5°
=sin40°sin245°/sin5°
=-sin40°sin65°/sin5°
sin210°+sin220°+sin230°+sin240°+sin250°+sin260°+sin270°+sin280
sin210°等于多少
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