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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)}. Apply the trigonometric identity: \sin\left(\theta \right)=\frac{\tan\left(\theta \right)}{\sqrt{1+\tan\left(\theta \right)^2}}. Divide fractions \frac{\cos\left(x\right)}{\frac{\tan\left(x\right)}{\sqrt{1+\tan\left(x\right)^2}}} 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: 1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2.