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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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