Тригонометрия

[hvyhg]

2cos80.sin(80+[tex]\alpha[/tex])=sin(80- [tex]\alpha[/tex])
да се намери алфа

[Knowledge Greedy]

2cos80.sin(80+α)=sin(80- α)

[tex]2sin\left (80^\circ+\alpha \right )cos80^\circ=sin(80^\circ-\alpha)[/tex]

sin[tex](80^\circ+\alpha + 80^\circ)+sin(80^\circ+\alpha - 80^\circ)=sin(80^\circ-\alpha)[/tex]

[tex]sin(160^\circ+\alpha)+sin\alpha = sin(80^\circ-\alpha)[/tex]

[tex]sin\alpha = sin(80^\circ-\alpha)-sin(20^\circ-\alpha)[/tex]

[tex]sin\alpha =2 sin\frac{80^\circ-\alpha-(20^\circ-\alpha)}{2}cos\frac{80^\circ-\alpha+20^\circ-\alpha}{2}[/tex]

[tex]sin\alpha =2 sin{30^\circ}cos(50^\circ -\alpha)[/tex]

[tex]sin\alpha =sin(40^\circ +\alpha)[/tex]

[tex]\alpha =40^\circ +\alpha[/tex] - н.р.

[tex]180^\circ - \alpha =40^\circ +\alpha[/tex]

[tex]2\alpha =140^\circ[/tex]

[tex]\alpha =70^\circ[/tex]