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Applying the trigonometric identity: $\sin\left(\theta \right)^2-\cos\left(\theta \right)^2 = -\cos\left(2\theta \right)$
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$\frac{-\cos\left(2x\right)}{1-\cot\left(x\right)^2}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (sin(x)^2-cos(x)^2)/(1-cot(x)^2). Applying the trigonometric identity: \sin\left(\theta \right)^2-\cos\left(\theta \right)^2 = -\cos\left(2\theta \right). Applying an identity of double-angle cosine: \cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2. Multiply the single term -1 by each term of the polynomial \left(1-2\sin\left(x\right)^2\right). Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}.