Respuesta :

Step-by-step explanation:

Recall that [tex]\sin^2x + \cos^2x = 1[/tex]

[tex](\sin x \sin y - \cos x \cos y)(\sin x \sin y + \cos x \cos y)[/tex]

[tex]= \sin^2 x \sin^2 y - \cos^2 x \cos^2 y[/tex]

[tex]= \sin^2 x (1 - \cos^2 y) - \cos^2 x \cos^2 y[/tex]

[tex]= \sin^2 x - \sin^2 x \cos^2y - \cos^2x \cos^2y[/tex]

[tex]= \sin^2x - (\sin^2x + \cos^2x)\cos^2y[/tex]

[tex]= \sin^2x - \cos^2y[/tex]