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]

Answer:

[A]    [tex]\frac{\sqrt{2 + \sqrt{3} } }{2}[/tex]

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