Use Identities to find the exact value.
-$$\cos \left( \frac { \pi } { 12 } \right)$$
A) $\frac { - \sqrt { 6 } - \sqrt { 2 } } { 4 }$
B) $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$
C) $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$
D) $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$

Question

Quizplus · Accepted Answer

$\cos \left( \frac { \pi } { 12 } \right)$ can be expressed using the half-angle identity as $\cos \left( \frac{\pi}{6} / 2 \right)$. Using the identity $\cos \left( \frac{\theta}{2} \right) = \pm \sqrt{\frac{1 + \cos(\theta)}{2}}$, and knowing that $\cos(\pi/6) = \sqrt{3}/2$, we find $\cos \left( \frac { \pi } { 12 } \right) = \sqrt{\frac{1 + \sqrt{3}/2}{2}} = \frac{\sqrt{6} + \sqrt{2}}{4}$.

Use Identities to Find the Exact Value cos⁡(π12)\cos \left( \frac { \pi } { 12 } \right)cos(12π​)

Use Identities to Find the Exact Value $\cos \left( \frac { \pi } { 12 } \right)$