Rezolvare:
Grupăm convenabil:
[tex](\cos 235^{\circ} + \cos 5^{\circ}) + \cos 115^{\circ} =[/tex]
Aplicăm formula
[tex]= 2 \cdot \cos \bigg(\dfrac{235^{\circ} - 5^{\circ}}{2}\bigg) \cdot \cos \bigg(\dfrac{235^{\circ}+5^{\circ}}{2}\bigg) + \cos 115^{\circ}\\[/tex]
[tex]= 2 \cdot \cos \dfrac{230^\circ}{2} \cdot \cos \dfrac{240^{\circ}}{2} + \cos 115^{\circ}[/tex]
[tex]= 2 \cdot \cos 115^{\circ} \cdot \cos 120^{\circ} + \cos 115^{\circ}[/tex]
[tex]= 2 \cdot \cos 115^{\circ} \cdot \cos (180^{\circ} - 60^{\circ}) + \cos 115^{\circ}[/tex]
Reducem la primul cadran
[tex]= 2 \cdot \cos 115^{\circ} \cdot \cos ( - 60^{\circ}) + \cos 115^{\circ}[/tex]
[tex]= 2 \cdot \cos 115^{\circ} \cdot \bigg(-\dfrac{1}{2}\bigg) + \cos 115^{\circ}[/tex]
[tex]= - \cos 115^{\circ} + \cos 115^{\circ}[/tex]
[tex]=\bf0[/tex]
⇒ egalitate demonstrată
✍ Reținem:
[tex]\boxed{\boldsymbol{ \cos \alpha + \cos \beta = 2 \cos \bigg(\dfrac{ \alpha - \beta}{2}\bigg)\cos \bigg(\dfrac{ \alpha + \beta}{2}\bigg)}}[/tex]
Despre reducerea funcțiilor trigonometrice la primul cadran https://brainly.ro/tema/11151478
