Question

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

Answer 1

Explanation:

`cos15=cos(30)/(2)` so the angle we will use in our identity is 30 degrees. The formula is

`cos(30)/(2)=\sqrt{(1+cos30)/(2) }` which simplifies to

`\sqrt{(1+(√(3) )/(2) )/(2) }` which simplifies to

`\sqrt{((2+√(3) )/(2) )/(2) }` which simplifies to

`\sqrt{(2+√(3) )/(4) }` which simplifies, finally, to

`\frac{\sqrt{2+√(3) } }{2}`, choice a.