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# Prove the trigonometric identity $\sec\left(x\right)^2\cot\left(x\right)-\cot\left(x\right)=\tan\left(x\right)$

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

$\sec\left(x\right)^2\cot\left(x\right)-\cot\left(x\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\sec\left(x\right)^2\cot\left(x\right)-\cot\left(x\right)$

Learn how to solve sum rule of differentiation problems step by step online. Prove the trigonometric identity sec(x)^2cot(x)-cot(x)=tan(x). Starting from the left-hand side (LHS) of the identity. Factor the polynomial \sec\left(x\right)^2\cot\left(x\right)-\cot\left(x\right) by it's greatest common factor (GCF): \cot\left(x\right). Apply the trigonometric identity: \sec\left(\theta \right)^2-1=\tan\left(\theta \right)^2. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \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: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.