Respuesta :

Panoyin
[sin(x) - cos(x)][sin(x) + cos(x)]
sin(x)[sin(x) + cos(x)] - cos(x)[sin(x) + cos(x)]
sin(x)[sin(x)] + sin(x)[cos(x)] - cos(x)[sin(x)] - cos(x)[cos(x)]
sin²(x) + sin(x)cos(x) - sin(x)cos(x) - cos²(x)
sin²(x) - cos²(x)
-cos(2x)
manissaha129

Answer:

Formula used:

  • (a-b)(a+b) = a²-b²
  • cos²(x)-sin²(x) = cos(2x)

[tex]→( \sin(x) - \cos(x))( \sin(x) + \cos(x)) \\ = { \sin }^{2}(x) - \cos^{2} (x) \\ = - ( { \cos }^{2}(x) - { \sin }^{2} (x)) \\ = \boxed{ - \cos(2x) }✓[/tex]

  • -cos(2x) is the right answer.