Respuesta :
Answer:
[tex]\sin 75\degree=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
Step-by-step explanation:
The haf-angle formula is given by:
[tex]\sin \frac{1}{2}\theta =\sqrt{\frac{1-\cos \theta}{2} }[/tex]
[tex]\sin 75\degree=\sin \frac{1}{2}(150\degree)[/tex].
This implies that:
[tex]\sin \frac{1}{2}(150\degree) =\sqrt{\frac{1-\cos 150\degree}{2} }[/tex]
[tex]\sin \frac{1}{2}(150\degree) =\sqrt{\frac{1--\frac{\sqrt{3}}{2}}{2}}[/tex]
[tex]\sin \frac{1}{2}(150\degree) =\sqrt{\frac{2+\sqrt{3}}{4}}[/tex]
We simplify the square root to obtain:
[tex]\sin \frac{1}{2}(150\degree)=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]