Use an identity to write the expression as a single trigonometric function or as a single number.
-$2 \cos ^ { 2 } 22.5 ^ { \circ } - 1$
A) $\sqrt { 3 }$

B) $\frac { \sqrt { 2 } } { 4 }$

C) $\frac { \sqrt { 3 } } { 3 }$

D) $\frac { \sqrt { 2 } } { 2 }$

Question

Use an identity to write the expression as a single trigonometric function or as a single number.
-$2 \cos ^ { 2 } 22.5 ^ { \circ } - 1$
A) $\sqrt { 3 }$

B) $\frac { \sqrt { 2 } } { 4 }$

C) $\frac { \sqrt { 3 } } { 3 }$

D) $\frac { \sqrt { 2 } } { 2 }$

Quizplus · Accepted Answer

This expression can be simplified using the cosine double angle identity, which is $\cos(2\theta) = 2\cos^2(\theta) - 1$. Here, $\theta = 22.5^\circ$, so the expression becomes $\cos(45^\circ)$, which equals $\frac{\sqrt{2}}{2}$.

Use an Identity to Write the Expression as a Single 2cos⁡222.5∘−12 \cos ^ { 2 } 22.5 ^ { \circ } - 12cos222.5∘−1

Use an Identity to Write the Expression as a Single $2 \cos ^ { 2 } 22.5 ^ { \circ } - 1$