solve tan 2x = 3 tan x?

Answer 1

Tan 2X = 2.(Tan X)/ ( 1 - Tan^2 X)

Now apply this to LHS.

2Tan X / ( 1 - Tan^2 X) = 3Tan X

Tan X ( 2 - 3(1- Tan^2 X) ) = 0 ( cross multiply by denominator )

Now

Tan X = 0 or -----------(A)
-1 + 3Tan^2 X = 0 ---- (B)

(A) ==> X = n*(pi)
(B) ==> Tan X = +/- (1/ sqrt(3) )
when positive ==> X = pi/6 + n*(pi)
when negative ==> X = -pi/6 + n*(pi)

i.e - (pi) is the radian constant
& 'n' is any integer

Cheers,
Codered

Answer 2

x=3/2

Answer 3

tan2x =2tanx/(1-tan^2x) so

2tan x= (3-3tan^2x)*tanx
tan x( 1-3tan^2x)=0
tan x = 0 x = n*pi(n any integer)
1-3tan^2x= 0 tan x= +-sqrt3 /x
x=pi/6+npi
x= 5pi/6 +n pi

Answer 4

tan 2x = 3 tan x

(sin 2x / cos 2x) = 3(sin x / cos x)

Use identities:

sin 2x = 2(sin x) (cos x)
cos 2x = cos^2 (x) - sin^2 (x)

(sin 2x / cos 2x) = 3(sin x / cos x)
becomes
(2(sin x) (cos x) / (cos^2 (x) - sin^2 (x))= 3(sin x / cos x)
(2(cos x) / (cos^2 (x) - sin^2 (x))= 3(1/ cos x)
2cos^2 (x) = 3(cos^2 (x) - sin^2 (x))
3sin^2 (x) = cos^2 (x)
tan^2 (x) = 1/3
and
tan x = 1 / sqrt(3)
arctan (1 / sqrt(3) ) = x

opposite = +/-1 and adjacent = +/-sqrt(3), so x = pi/6 or 7pi/6
if 0<=x<=2pi

Answer 5

X=1

Tan 2x=3tan x

Tan 2x=3tan x
+x -x

Tan 3x=3Tan

x=1

Answer 6

x=1.5