求求下列各式的值 (1)sin^262°+tan54°tan45°tan36°+sin^28° (2)tan1°tan2
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/09/15 05:33:14
求求下列各式的值 (1)sin^262°+tan54°tan45°tan36°+sin^28° (2)tan1°tan2°tan3°……tan89°
(1)
sin^2(62°)+tan54°tan45°tan36°+sin^2(28° )
= sin^2(62°) + tan54°tan45°tan(90°-54°)+sin^2(90°-62° )
= sin^2(62°) + tan54°tan45° cot54° + cos^2(62° )
= sin^2(62°) + cos^2(62° )+ tan54°cot54° tan45°
= 1 + 1*1
= 2
(2)
tan1°tan2°tan3°……tan89°
= tan1°tan89° * tan2°tan88° *……tan44°tan46° * tan45°
= tan1°cot1° * tan2°cot2° *……tan44°cot44° * tan45°
= 1*1*...181
= 1
sin^2(62°)+tan54°tan45°tan36°+sin^2(28° )
= sin^2(62°) + tan54°tan45°tan(90°-54°)+sin^2(90°-62° )
= sin^2(62°) + tan54°tan45° cot54° + cos^2(62° )
= sin^2(62°) + cos^2(62° )+ tan54°cot54° tan45°
= 1 + 1*1
= 2
(2)
tan1°tan2°tan3°……tan89°
= tan1°tan89° * tan2°tan88° *……tan44°tan46° * tan45°
= tan1°cot1° * tan2°cot2° *……tan44°cot44° * tan45°
= 1*1*...181
= 1
tan54°×tan36°=1,可以不用计算器算吗,写下
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