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
=>...
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giorgiana1976 | Student
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
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