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

Question

Quizplus · Accepted Answer

Using the addition formula for cosine, we have:
$$\cos \left(\frac{\pi}{12}\right)=\cos \left(\frac{\pi}{6}-\frac{\pi}{4}\right)=\cos \frac{\pi}{6}\cos\frac{\pi}{4}-\sin\frac{\pi}{6}\sin\frac{\pi}{4}=\frac{\sqrt{3}}{2}\cdot\frac{\sqrt{2}}{2}-\frac{1}{2}\cdot\frac{\sqrt{2}}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}$$
Therefore, the answer is D.

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

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