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Expand the fraction $\frac{\csc\left(x\right)-\sin\left(x\right)}{\cot\left(x\right)}$ into $2$ simpler fractions with common denominator $\cot\left(x\right)$
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$\frac{\csc\left(x\right)}{\cot\left(x\right)}+\frac{-\sin\left(x\right)}{\cot\left(x\right)}$
Learn how to solve limits by direct substitution problems step by step online. Simplify the trigonometric expression (csc(x)-sin(x))/cot(x). Expand the fraction \frac{\csc\left(x\right)-\sin\left(x\right)}{\cot\left(x\right)} into 2 simpler fractions with common denominator \cot\left(x\right). Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Divide fractions \frac{\csc\left(x\right)}{\frac{\cos\left(x\right)}{\sin\left(x\right)}} 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}. Applying the trigonometric identity: \sin\left(\theta \right)\csc\left(\theta \right) = 1.