Question

x+y+z = π, tan x.tan z = 2 and tan y.tan z =18, then tan² z = ?

Answer 1

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Trigonometry (mathematics): If x+y+z= π, tan x.tan y=18, tan y.tan z=2. What is tan y?


change is x,y,z areinterchanged






tan x=18/tan y.......(1)



Replace z=180-(x+Y) in the second equation and we ge

tan y.tan (180 - (x+y))=2

tan y.tan (x+y) = -2

tan y. (tan x + tan y)/1-tan x.tan y = -2

(tan y.tan x + tan^2 y)/(1-tan x.tan y) = -2

Let tan y = p

18 + p^2=-2(1-18)

p^2=34-18

p=+-4
Thus tan y = 4
tan ^2 y =16
assuming x,y,z are angles of a triangle