Complete the identity.
-$\sin ^ { 4 } x - \cos ^ { 4 } x =$ ?
A) $1 - 2 \cos ^ { 2 } x$
B) $1 + 2 \cos ^ { 2 } x$
C) $1 + 2 \sin ^ { 2 } x$
D) $1 - 2 \sin ^ { 2 } x$

Question

Quizplus · Accepted Answer

This identity can be simplified by factoring it as a difference of squares: $\sin^4 x - \cos^4 x = (\sin^2 x + \cos^2 x)(\sin^2 x - \cos^2 x)$. Using the Pythagorean identity $\sin^2 x + \cos^2 x = 1$ and the identity $\sin^2 x - \cos^2 x = 1 - 2\cos^2 x$, we get $1(1 - 2\cos^2 x) = 1 - 2\cos^2 x$.

Complete the Identity sin⁡4x−cos⁡4x=\sin ^ { 4 } x - \cos ^ { 4 } x =sin4x−cos4x=

Complete the Identity $\sin ^ { 4 } x - \cos ^ { 4 } x =$