Convert the expression. $$\cos 4 \alpha$$
A) $\cos ^ { 2 } 2 \alpha - \sin ^ { 2 } 2 \alpha$
B) $\cos ^ { 2 } 2 \alpha + \sin ^ { 2 } 2 \alpha$
C) $\cos ^ { 4 } 2 \alpha + \sin ^ { 4 } 2 \alpha$
D) $\cos ^ { 4 } 2 \alpha - \sin ^ { 4 } 2 \alpha$
E) $\cos ^ { 4 } 2 \alpha - \sin ^ { 2 } 2 \alpha$

Question

Convert the expression.​ $$\cos 4 \alpha$$ ​
A)​ $\cos ^ { 2 } 2 \alpha - \sin ^ { 2 } 2 \alpha$
B)​ $\cos ^ { 2 } 2 \alpha + \sin ^ { 2 } 2 \alpha$
C)​ $\cos ^ { 4 } 2 \alpha + \sin ^ { 4 } 2 \alpha$
D)​ $\cos ^ { 4 } 2 \alpha - \sin ^ { 4 } 2 \alpha$
E)​ $\cos ^ { 4 } 2 \alpha - \sin ^ { 2 } 2 \alpha$

Quizplus · Accepted Answer

The correct expression is derived from the double angle formula for cosine, $\cos 2\theta = \cos^2 \theta - \sin^2 \theta$, applied twice.

Convert the Expression cos⁡4α\cos 4 \alphacos4α ​ A)​ cos⁡22α−sin⁡22α\cos ^ { 2 } 2 \alpha - \sin ^ { 2 } 2 \alphacos22α−sin22α

Convert the Expression $\cos 4 \alpha$
A) $\cos ^ { 2 } 2 \alpha - \sin ^ { 2 } 2 \alpha$