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Prove the trigonometric identity $\cot\left(x\right)^2=\left(\csc\left(x\right)-1\right)\left(\csc\left(x\right)+1\right)$

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Solution

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Final answer to the problem

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
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Starting from the right-hand side (RHS) of the identity

$\left(\csc\left(x\right)-1\right)\left(\csc\left(x\right)+1\right)$

Learn how to solve factor by difference of squares problems step by step online.

$\left(\csc\left(x\right)-1\right)\left(\csc\left(x\right)+1\right)$

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Learn how to solve factor by difference of squares problems step by step online. Prove the trigonometric identity cot(x)^2=(csc(x)-1)(csc(x)+1). Starting from the right-hand side (RHS) of the identity. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Applying the trigonometric identity: \csc\left(\theta \right)^2-1 = \cot\left(\theta \right)^2. Since we have reached the expression of our goal, we have proven the identity.

Final answer to the problem

true

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Main Topic: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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