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

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##  Step-by-step Solution 

How should I solve this problem?

• Prove from LHS (left-hand side)
• Prove from RHS (right-hand side)
• Express everything into Sine and Cosine
• Exact Differential Equation
• Linear Differential Equation
• Separable Differential Equation
• Homogeneous Differential Equation
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
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Starting from the left-hand side (LHS) of the identity

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

Learn how to solve problems step by step online.

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

Learn how to solve 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}.

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##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more