Answer:
Step-by-step explanation:
[tex]cos15=cos\frac{30}{2}[/tex] so the angle we will use in our identity is 30 degrees. The formula is
[tex]cos\frac{30}{2}=\sqrt{\frac{1+cos30}{2} }[/tex] which simplifies to
[tex]\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }[/tex] which simplifies to
[tex]\sqrt{\frac{\frac{2+\sqrt{3} }{2} }{2} }[/tex] which simplifies to
[tex]\sqrt{\frac{2+\sqrt{3} }{4} }[/tex] which simplifies, finally, to
[tex]\frac{\sqrt{2+\sqrt{3} } }{2}[/tex], choice a.
