If `(tanx)/2=(tany)/3=(tanz)/5,x+y+z=pia n dtan^2x+tan^2y+tan^2z=(38)/Kt h a nK=_________`

Answer

3

Explanation

`tan x = 2t, tan y = 3t, tan z = 5t`
Also `x +y +z= pi`
`therefore tan x + tany + tan z = tan x tan y tanz`
`rArr t^(2) = (1)/(3)`
`rArr tan ^(2) x + tan ^(2) y + tan^(2) z = t ^(2) ( 4+ 9 + 25) = 38t^(2), `
`therefore K = 3`