# document.write (document.title)

 Math Help > Trigonometry > Trig Equivalences > Continued Fraction Tan

# Trigonometric Equivalences -- Continued Fraction for Tan nx

 Tan 2x = 2 tan x 1- (2²-1²)tan²x 3
 Tan 3x = 3 tan x 1- (3²-1²)tan²x 3- (3²-2²)tan²x 5
 Tan 4x = 4 tan x 1- (4²-1²)tan²x 3- (4²-2²)tan²x 5- (4²-3�)tan�x 7

The continued fractions terminate because the next term would be zero (expressions like 4²-4²).  In fact the expansion holds for non-integer values of n as well, but does not terminate.

### Related Pages in this website

Trig Identities

Special Angles

Sin or Cos 3x, 4x, etc. -- trig functions of any multiple of an angle.

d/dx (sin x) = cos x, in the calculus section of this website

Hyperbolic Functions -- sinh(x) and cosh(x), which, together with exp(x) and the circular functions sin(x) and cos(x) form a family of functions.

Table of Integrals -- derivations of various special integrals requires extensive use of the trig identities on this page.

The webmaster and author of this Math Help site is Graeme McRae.