Question

Uzasadnij, że zachodzi równość:
-cos150° * cos90° - sin150° * sin90° = cos120°
PLIS PILNE DAM NAJ!

Answer 1

Szczegółowe wyjaśnienie:

Korzystamy ze wzorów redukcyjnych:

[tex]sin150^{0} = sin(90^{0}+60^{0}) = sin60^{0} = \frac{1}{2}\\\\cos120^{0} = cos(90^{0}+30^{0}) = -sin30^{0} = -\frac{1}{2}\\\\oraz:\\\\cos90^{0} = 0\\\\sin90^{0} = 1[/tex]

[tex]L = -cos150^{0}\cdot cos90^{0}-sin150^{0}\cdot sin90^{0} =-cos150^{0}\cdot0-sin(90^{0}+60^{0})\cdot1=\\\\=0-(cos60^{0})\cdot1 = -cos60^{0} = \boxed{-\frac{1}{2}}[/tex]

[tex]P = cos120^{0} = cos(90^{0}+30^{0}) = -sin30^{0} = \boxed{-\frac{1}{2}}[/tex]

[tex]\boxed{L = P}[/tex]

[tex]c.n.d.[/tex]