Use identities to find the indicated value for each angle measure.
-$2 \cos ^ { 2 } 22.5 ^ { \circ } - 1$
A) $\frac { \sqrt { 2 } } { 2 }$
B) $\frac { \sqrt { 3 } } { 3 }$
C) $\sqrt { 3 }$
D) $\frac { \sqrt { 2 } } { 4 }$

Question

Quizplus · Accepted Answer

The expression $2 \cos ^ { 2 } 22.5 ^ { \circ } - 1$ can be recognized as the double angle identity for cosine, which is $\cos(2\theta) = 2\cos^2(\theta) - 1$. Therefore, the expression simplifies to $\cos(45^\circ)$, which equals $\frac{\sqrt{2}}{2}$.

Use Identities to Find the Indicated Value for Each Angle 2cos⁡222.5∘−12 \cos ^ { 2 } 22.5 ^ { \circ } - 12cos222.5∘−1

Use Identities to Find the Indicated Value for Each Angle $2 \cos ^ { 2 } 22.5 ^ { \circ } - 1$