Question

Evaluate cos^2 (n/12)

Answer 1

Answer:

$\frac{2+\sqrt{3} }{4}$

Step-by-step explanation:

We can use the identity $Cos^2(x)=\frac{1}{2}+\frac{1}{2}Cos(2x)$ to write it as:

$Cos^2(\frac{\pi}{12})=\frac{1}{2}+\frac{1}{2}Cos(2(\frac{\pi}{12}))\\=\frac{1}{2}+\frac{1}{2}Cos(\frac{\pi}{6})\\=\frac{1}{2}+\frac{1}{2}(\frac{\sqrt{3} }{2})\\=\frac{1}{2}+\frac{\sqrt{3} }{4}\\=\frac{2+\sqrt{3} }{4}$

Note: The value of $Cos(\frac{\pi}{6})$  is  $\frac{\sqrt{3} }{2}$

The answer is the 2nd one, $\frac{2+\sqrt{3} }{4}$