===== Auxiliares =====

==== tan x + cot x ====
  * <m 15>tan x + cot x ~=~  sec x . csc x</m>
  * <m 15>tan^2 x + cot^2 x ~=~  sec^2 x . csc^2 x</m>

==== sec x + csc x ====
  * <m 15>sec^2 x + csc^2 x ~=~  sec^2 x . csc^2 x</m>, α =/= nPI/2 n ∈ Z

==== sen x + cos x ====
  * <m 15>(sin x ± cos x)^2 ~=~  1 ± 2 sin x . cos x</m>
  * <m 15>(sin x + cos x + 1)(sin x + cos x - 1) ~=~  2 sin x . cos x</m>
  * <m 15>(1 ± sin x ± cos x )^2 ~=~  2 (1 ± sin x)(1 ± cos x)</m>

==== sin^4 x ====

  * <m 15>8 sin^4 x ~=~  3 - 4 cos 2x + cos 4x</m>
  * <m 15>8 cos^4 x ~=~  3 + 4 cos 2x + cos 4x</m>

==== sin^4 x + cos^4 x ====

  * <m 15>sin^4 x + cos^4 x ~=~  1 - 2 sin^2 x . cos^2 x</m>
  * <m 15>sin^4 x + cos^4 x ~=~  3/4 + 1/4 {cos 4x}</m>

==== sin^4 - cos^4 ====

  * <m 15>sin^4 x - cos^4 ~=~  sin^2 x - cos^2 x</m>
  * <m 15>sec^4 x - tan^4 ~=~  sec^2 x + tan^2 x</m>
  * <m 15>csc^4 x - cot^4 ~=~  csc^2 x + cot^2 x</m>

==== sin^6 x + cos^6 x ====

  * <m 15>sin^6 x + cos^6 x ~=~  1 - 3sin^2 x . cos^2 x</m>
  * <m 15>sin^6 x + cos^6 x ~=~  5/8 + 3/8 {cos 4x}</m>

==== Sin Clasificar ====

  * <m 15>4 sin^3(x) = 3sin(x) - sin(3x)</m>
  * <m 15>4 cos^3(x) = 3cos(x) + cos(3x)</m>

Se infiere de [[academia:numeros:trigonometria:angulo_doble#cos_2x|Cos 2x]] : 

  * <m 15>2.sin^2(x) = 1 - cos(2x)</m>
  * <m 15>2.cos^2(x) = 1 + cos(2x)</m>