lmrrege
lmrrege lmrrege
  • 22-01-2019
  • Mathematics
contestada

cos x cos(-x)-sin x sin(-x)=1 please certify the identity with steps!!!!!

Respuesta :

carlosego
carlosego carlosego
  • 22-01-2019

Step-by-step explanation:

To answer this problem we must know the following properties.

[tex]cos(-x) = cos(x)[/tex] even function

[tex]sin(-x) = -sin(x)[/tex] odd function

[tex]cos^2(x) - sin(x)sin(-x) = 1[/tex]   Because..........[tex]cos(x) = cos(-x)[/tex]

[tex]cos^2(x) + sin^2(x) = 1[/tex]  Because.......... [tex]sin(-x) = -sin(x)[/tex]

By definition

[tex]cos^2 (x) + sin^2 (x) = 1[/tex]

Then, the property is demonstrated:

[tex]cos(x)cos(-x) - sin(x)sin(-x) = 1[/tex]



Answer Link

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