Need som help with tan (1 Viewer)

[Leopolder]

Hi,
I need some help too solve this one: tan3x=tanx

Thanks

 

[sasquatch]

Dunno what range you want, but from 0<=x<=2pi,

tan3x = tanx
tan(2x + x) = tanx
(tan2x + tanx)/(1-tanxtan2x) = tanx
tan2x + tanx = tanx - tan²xtan2x
tan2x = - tan²xtan2x
tan²xtan2x + tan2x = 0
tan2x(tan²x + 1) = 0
tan2x = 0, tan²x = -1 (no solution for this part)

2x = 0, pi, 2pi, 3pi, 4pi (0 <= x <= 4pi)
x = 0, pi/2, pi, 3pi/2, 2pi

but function is undefined at (pi/2, 3pi/2)

so x = 0, pi, 2pi

 

[Riviet]

If the question dosen't specify a range, then you would use the general solution, x=pi.n where n is an integer.

 

[ice ken]

leopolder hsc 2004? u doing yr 12 for the third time??????