Question

Use a half-angle identity to find the exact value of cos 15º.

Answer 1

Answer:

Step-by-step explanation:

$cos15=cos\frac{30}{2}$ so the angle we will use in our identity is 30 degrees. The formula is

$cos\frac{30}{2}=\sqrt{\frac{1+cos30}{2} }$ which simplifies to

$\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }$ which simplifies to

$\sqrt{\frac{\frac{2+\sqrt{3} }{2} }{2} }$ which simplifies to

$\sqrt{\frac{2+\sqrt{3} }{4} }$ which simplifies, finally, to

$\frac{\sqrt{2+\sqrt{3} } }{2}$, choice a.