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tan10tan20+tan20tan60+tan70tan10=?
题目详情
tan10tan20+tan20tan60+tan70tan10=?
▼优质解答
答案和解析
tan10tan20+tan20tan60+tan70tan10
= (tan10+tan60)tan20 + tan70tan10
= tan70*(1-tan10tan60)*tan20 + tan70tan10
= tan70 (tan20+tan10- tan10tan20tan60)
= tan70 [tan30(1-tan10tan20)- tan10tan20tan60]
= tan70 tan30 - tan10tan20tan70(tan30+tan60)
= tan70 tan30 - tan10(tan30+tan60)
= tan30(tan70-tan10) - tan10tan60
= tan30tan60*(1+tan70tan10) - tan10tan60
= 1+tan70tan10- tan10tan60
= 1+ tan10(tan70-tan60)
= (tan10+tan60)tan20 + tan70tan10
= tan70*(1-tan10tan60)*tan20 + tan70tan10
= tan70 (tan20+tan10- tan10tan20tan60)
= tan70 [tan30(1-tan10tan20)- tan10tan20tan60]
= tan70 tan30 - tan10tan20tan70(tan30+tan60)
= tan70 tan30 - tan10(tan30+tan60)
= tan30(tan70-tan10) - tan10tan60
= tan30tan60*(1+tan70tan10) - tan10tan60
= 1+tan70tan10- tan10tan60
= 1+ tan10(tan70-tan60)
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