Question

Find the exact value by using a half-angle identity.

cos 5pi/12

How would I solve this?

Answer 1

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

Answer 2

Thank you so much!

Answer 3

yw