Find the exact value by using a half-angle identity.
-$\cos 165 ^ { \circ }$
A) $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$
B) $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$
C) $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$
D) $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$

Question

Quizplus · Accepted Answer

The angle 165° can be expressed as 330°/2. Using the half-angle identity for cosine, $\cos(165°) = -\sqrt{\frac{1 + \cos(330°)}{2}}$. Since $\cos(330°) = \sqrt{3}/2$, the expression becomes $-\sqrt{\frac{1 + \sqrt{3}/2}{2}} = -\frac{1}{2}\sqrt{2 + \sqrt{3}}$.

Find the Exact Value by Using a Half-Angle Identity cos⁡165∘\cos 165 ^ { \circ }cos165∘

Find the Exact Value by Using a Half-Angle Identity $\cos 165 ^ { \circ }$