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