We are given 4 cos x + 2 sin x = 0, we have to find tan 2x
4 cos x + 2 sin x = 0
=> 4 cos x = - 2sin x
=> sin x/cos x = 4/-2
=> tan x = -2
tan 2x = 2*tan x/[1-(tan x)^2]
=> 2*(-2)/(1 - (-2)^2)
=> -4 / (1 - 4)
=> -4/ -3
=> 4/3
The required value of tan 2x = 4/3
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