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

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true

##  Step-by-step Solution 

How should I solve this problem?

• Prove from RHS (right-hand side)
• Prove from LHS (left-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
Can't find a method? Tell us so we can add it.
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Starting from the right-hand side (RHS) of the identity

$\csc\left(x\right)+\cot\left(x\right)$
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Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$

$\csc\left(x\right)+\frac{\cos\left(x\right)}{\sin\left(x\right)}$
Why does cot(x) = cos(x)/sin(x) ?

Learn how to solve trigonometric identities problems step by step online.

$\csc\left(x\right)+\cot\left(x\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)/(1-cos(x))=csc(x)+cot(x). Starting from the right-hand side (RHS) of the identity. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.

true

##  Explore different ways to solve this problem

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###  Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.