tanx+tany=25 cotx+coty=30,那么tan(x+y)=?

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tanx+tany=25 cotx+coty=30,那么tan(x+y)=?
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tanx+tany=25 cotx+coty=30,那么tan(x+y)=?
tanx+tany=25 cotx+coty=30,那么tan(x+y)=?

tanx+tany=25 cotx+coty=30,那么tan(x+y)=?
cotx+coty=30
1/tanx +1/tany=30
(tanx+tany)/tanxtany=30
25/tanxtany=30
tanxtany=25/30=5/6,
tan(x+y)
=(tanx+tany)/(1-tanxtany)
=25/(1-5/6)
=150

cotx+coty
=1/tanx+1/tany
=(tanx+tany)/(tanxtany)
=30
所以 tanxtany=25/30=5/6
所以 tan(x+y)=(tanx+tany)/(1-tanxtany)=25/(1-5/6)=150