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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 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: \cos\left(2\theta \right)=\frac{2\tan\left(\theta \right)}{1+\tan\left(\theta \right)^2}. Multiply -1 times 2. Divide fractions \frac{\frac{-2\tan\left(x\right)}{1+\tan\left(x\right)^2}}{1-\cot\left(x\right)^2} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.