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 Skip Navigation LinksMath 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.

Internet references

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.

 

 


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