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

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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 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

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

$\sec\left(x\right)\left(\cot\left(x\right)-1\right)+\csc\left(x\right)\left(1-\tan\left(x\right)\right)$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity sec(x)(cot(x)-1)+csc(x)(1-tan(x))=2(csc(x)-sec(x)). Starting from the left-hand side (LHS) of the identity. Multiply the single term \sec\left(x\right) by each term of the polynomial \left(\cot\left(x\right)-1\right). Simplify \cot\left(x\right)\sec\left(x\right) by applying trigonometric identities. Multiply the single term \csc\left(x\right) by each term of the polynomial \left(1-\tan\left(x\right)\right).

Final answer to the problem

true

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Main Topic: Proving Trigonometric Identities

To prove a trigonometric identity, you have to show that one side of the equation can be transformed into the other side.

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