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Starting from the left-hand side (LHS) of the identity
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$\frac{\cos\left(x\right)\cot\left(x\right)}{1-\sin\left(x\right)}-1$
Learn how to solve differential calculus problems step by step online. Prove the trigonometric identity (cos(x)cot(x))/(1-sin(x))-1=csc(x). Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by \cos\left(x\right). Divide fractions \frac{\frac{\cos\left(x\right)^2}{\sin\left(x\right)}}{1-\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}.