Question

use half angle identity to evaluate cos 11pi divided by 12

Answer 1

\[2\cos^2 \frac{ 11 \pi }{ 12 }=1+\cos 2*\frac{ 11 \pi }{ 12 }=1+\cos \frac{ 11 \pi }{ 6 }=1+\cos \left( 2 \pi-\frac{ \pi }{ 6 } \right)\]
\[=1+\cos \frac{ \pi }{ 6}=1+\frac{ \sqrt{3} }{ 2}\]

Answer 2

\[\cos \frac{ 11 \pi }{ 12 }=\cos \left( \pi-\frac{ \pi }{ 12 } \right)=-\cos \frac{ \pi }{ 12 }=-\cos \left( \frac{ \pi }{ 3 }-\frac{ \pi }{ 4 } \right)\]
\[=-\left( \cos \frac{ \pi }{ 3 } \cos \frac{ \pi }{ 4 } +\sin \frac{ \pi }{ 3 } \sin \frac{ \pi }{ 4 } \right)=?\]