Answer:
- [tex]\frac{\sqrt{2+\sqrt{3} } }{2}[/tex]
Step-by-step explanation:
using the half angle formula
cos([tex]\frac{x}{2}[/tex] ) = ± [tex]\sqrt{\frac{1+cosx}{2} }[/tex]
cos195° = cos(180 + 15)° = - cos15°
then
cos15° = cos ([tex]\frac{30}{2}[/tex] ) = [tex]\sqrt{\frac{1+cos30}{2} }[/tex] = [tex]\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }[/tex] = [tex]\sqrt{\frac{2+\sqrt{3} }{4} }[/tex] = [tex]\frac{\sqrt{2+\sqrt{3} } }{2}[/tex]
then
cos195° = - cos15° = - [tex]\frac{\sqrt{2+\sqrt{3} } }{2}[/tex]
