# Given 4cosx+2sinx=0 find tan2x

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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**

If we'll divide the constraint from enunciation by cos x, the expression will become:

4 + 2sin x/cos x = 0

We'll subtract 4:

2sin x/cos x = -4

sin x/cos x = -4/2

sin x/cos x = -2

But sin x/cos x = tan x

tan x = -2

We'll write tan 2x:

tan 2x=tan (x+x)

tan 2x = (tan x+ tan x)/[1-(tan x)^2]

tan 2x = 2tan x/[1-(tan x)^2]

We'll substitute tan x = -2

tan 2x = 2*(-2)/[1-(-2)^2]

tan 2x = -4/(1-4)

tan 2x = -4/-3

**tan 2x = 4/3**