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If tan x + tan y = 25 and cot x + cot y = 30, then the value of tan(x+y)= ??

If tan x + tan y = 25 and cot x + cot y = 30, then the value of tan(x+y)= ??
 

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1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
tanx + tany = sin(x+y)/cosx cosy ----- (1)
cotx + cot y = sin(x+y)/sinx siny -------(2)
divide (1)/ (2), we have
[tanx + tany] / [cotx + cot y] = [sin(x+y)/cosx cosy]/[sin(x+y)/sinx siny] = 25/30
=> sinx siny/cosx cosy = 5/6
=> tanx tany= 5/6
So, tan(x + y) = (tanx + tany) /(1-tanxtany) = 25/(1-5/6) = 150
 
 
 
 

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