## anonymous one year ago Find the exact value by using a half-angle identity. cos 5pi/12 How would I solve this?

1. anonymous

$2 \cos ^2\frac{ 5 \pi }{ 12 }=1+\cos 2*\frac{ 5 \pi }{ 12 }=1+\cos \frac{ 5 \pi }{ 6 }=1+\cos \left( \pi-\frac{ \pi }{ 6 } \right)$ $=1-\cos \frac{ \pi }{ 6 }=1-\frac{ \sqrt{3} }{ 2 }=\frac{ 2-\sqrt{3} }{ 2 }$ $\cos \frac{ 5 \pi }{ 12 }=\sqrt{\frac{ 2-\sqrt{3} }{ 4 }}=\frac{ \sqrt{2-\sqrt{3}} }{ 2 }$

2. anonymous

Thank you so much!

3. anonymous

yw