Ensino Médio ⇒ (Aref) Trigonometria Tópico resolvido

[gabriel93]

Simplifique a expressão:

[tex3]y = senx(2cos2x +2cos4x +2cos6x +1)[/tex3]


Resposta do gabarito:

Resposta

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[tex3]y = sen7x[/tex3]

[Vinisth]

Olá gabriel93,

[tex3]y = \sin (x)(2\cos (2x) +2\cos (4x) +2\cos (6x) +1)[/tex3]
[tex3]y = 2\sin (x)\cos (2x) +2\sin (x)\cos (4x) +2\sin (x)\cos (6x) +\sin (x)[/tex3]

Agora usemos prostaférese e temos :

[tex3]\boxed{2\sin (x)\cos (2x) = \sin(3x)-\sin(x)}[/tex3]
[tex3]\boxed{2\sin (x)\cos (4x) = \sin(5x)-\sin(3x)}[/tex3]
[tex3]\boxed{2\sin (x)\cos (6x) = \sin(7x)-\sin(5x)}[/tex3]

[tex3]y = \cancel{\sin(3x)}-\cancel{\sin(x)} +\cancel{\sin(5x)}-\cancel{\sin(3x)} +\sin(7x)-\cancel{\sin(5x)} +\cancel{\sin x}[/tex3]

Logo :

[tex3]\boxed{\boxed{\boxed{y= \sin(7x)}}}[/tex3]

Abraço.