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

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true

##  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
• Load more...
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Starting from the left-hand side (LHS) of the identity

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

Learn how to solve differential equations problems step by step online.

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

Learn how to solve differential equations problems step by step online. Prove the trigonometric identity (sec(x)-1)/(1-cos(x))=sec(x). Starting from the left-hand side (LHS) of the identity. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Simplify the fraction \frac{\frac{1-\cos\left(x\right)}{\cos\left(x\right)}}{1-\cos\left(x\right)} by 1-\cos\left(x\right).

true

##  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

###  Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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