Simplify the expression.
-$1 - 2 \sin ^ { 2 } 2 x$
A) $\frac { 1 } { 2 } \sin 16 x$
B) $\cos 8 x$
C) $\cos 4 x$
D) $2 \sin 4 x$

Name: Simplify the expression. -$1 - 2 \sin ^ { 2 } 2 x$ A) $\frac { 1 } { 2 } \sin 16 x$ B) $\cos 8 x$ C) $\cos 4 x$ D) $2 \sin 4 x$
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Question

Quizplus · Accepted Answer

Using the double angle formula for cosine, $1 - 2 \sin^2 2x = \cos 4x$. This is because the identity $1 - 2 \sin^2 \theta = \cos 2\theta$ can be applied with $\theta = 2x$, resulting in $\cos 4x$.

Simplify the Expression 1−2sin⁡22x1 - 2 \sin ^ { 2 } 2 x1−2sin22x

Simplify the Expression $1 - 2 \sin ^ { 2 } 2 x$