If `(tanx)/2=(tany)/3=(tanz)/5,x+y+z=pi` and `tan^2x+tan^2y+tan^2z=(38)/K` then K=_________`

Explanation

Aas `x+y+z = pi`,

`:. tanx+tany+tanz = tanxtanytanz->(1)`

Let `tanx/2 = tany/3 = tanz/5 = k`

`=>tanx = 2k, tany = 3k, tanz = 5k`

Putting these values in (1),

`2k+3k+5k = 2k(3k)(5k)`

`=>10k = 30k^3`

`=>k^2 = 1/3`

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