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