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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). Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}. Combine 1+\frac{-\cos\left(x\right)^2}{\sin\left(x\right)^2} in a single fraction. Divide fractions \frac{-\cos\left(2x\right)}{\frac{-\cos\left(x\right)^2+\sin\left(x\right)^2}{\sin\left(x\right)^2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.