Ensino Médio ⇒ (UFJF-MG) Trigonometria Tópico resolvido

[dark123]

04. (UFJF-MG) Sendo x + y = 60°, o valor de (cos x + cos y)2 + (sen x – sen y)2 – 2 é:

A) -2

B) -1/2

C) 0

D) 1

E) 2

Gabarito: D

[petras]

dark123,

[tex3]\mathtt{
(cos x + cos y)^2 + (sen x – sen y)^2 – 2=
cos^2x+cos^2y+2cosxcosy+sen^2x+sen^2y-2senxseny-2=\\
sen^2x+cos^2x+sen^2+cos^2y+ 2(cosxcosy-senxseny)-2=\\
1+1+2cos(x+y)-2 = \\
2cos60^o = 2.\frac{1}{2} =\boxed{1}\huge\color{green}\checkmark

}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathtt{
(cos x + cos y)^2 + (sen x – sen y)^2 – 2=
cos^2x+cos^2y+2cosxcosy+sen^2x+sen^2y-2senxseny-2=\\
sen^2x+cos^2x+sen^2+cos^2y+ 2(cosxcosy-senxseny)-2=\\
1+1+2cos(x+y)-2 = \\
2cos60^o = 2.\frac{1}{2} =\boxed{1}\huge\color{green}\checkmark

}[/tex3]