Apply the trigonometric identity: $\sin\left(\theta \right)^4-\cos\left(\theta \right)^4$$=1-2\cos\left(\theta \right)^2$
$1-2\cos\left(x\right)^2$
2
Applying the trigonometric identity: $1-2\cos\left(\theta \right)^2 = -\cos\left(2\theta \right)$
$-\cos\left(2x\right)$
Final answer to the problem
$-\cos\left(2x\right)$
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The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.