Answer:
A
Step-by-step explanation:
Think of a value on the unit circle that is double of 165.
330 is that so we can use the double Angle Identity
[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]
Alpha is 330
so
[tex] \sin(165) = \sqrt{ \frac{1 - \cos(330) }{2} } [/tex]
[tex] \sin(165) = \sqrt{ \frac{1 - \frac{ \sqrt{3} }{2} }{2} } [/tex]
[tex] \sin(165) = \sqrt{ \frac{ \frac{2 - \sqrt{3} }{2} }{2} } [/tex]
[tex] \sin(165) = \sqrt{ \frac{2 - \sqrt{3} }{4} } [/tex]
[tex] \sin(165) = \frac{ \sqrt{2 - \sqrt{3} } }{2} [/tex]
