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Multiply both sides of the equation by $\sin$
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$\sin\left(x\right)\left(\frac{1-\cos\left(x\right)}{\sin\left(x\right)}+\frac{-\sin\left(x\right)}{1-\cos\left(x\right)}\right)=2\sin\left(x\right)\csc\left(x\right)\cot\left(x\right)$
Learn how to solve problems step by step online. Prove that (1-cos(x))/sin(x)+(-sin(x))/(1-cos(x))=2csc(x)cot(x) is not an identity. Multiply both sides of the equation by \sin. Applying the trigonometric identity: \sin\left(\theta \right)\csc\left(\theta \right) = 1. Combine \frac{1-\cos\left(x\right)}{\sin\left(x\right)}+\frac{-\sin\left(x\right)}{1-\cos\left(x\right)} in a single fraction. Multiplying the fraction by \sin\left(x\right).