Prove the trigonometric identity $\frac{\sin\left(-x\right)}{1-\cos\left(-x\right)}=-\csc\left(x\right)-\cot\left(x\right)$

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$\frac{-\sin\left(x\right)}{1-\cos\left(x\right)}=-\csc\left(x\right)-\cot\left(x\right)$

Learn how to solve simplify trigonometric expressions problems step by step online. Prove the trigonometric identity sin(-x)/(1-cos(-x))=-csc(x)-cot(x). Start by simplifying the left side of the identity: \frac{\sin\left(-x\right)}{1-\cos\left(-x\right)}. Starting from the left-hand side (LHS) of the identity. Multiply and divide the fraction \frac{-\sin\left(x\right)}{1-\cos\left(x\right)} by the conjugate of it's denominator . Apply the trigonometric identity: 1-\cos\left(\theta \right)^2=\sin\left(\theta \right)^2.