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Prove the trigonometric identity $\csc\left(x\right)\left(\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)\right)=\frac{\cos\left(x\right)}{\sin\left(x\right)}$

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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.

$\csc\left(x\right)\left(\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)\right)$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)(sec(x)-tan(x)sin(x))=cos(x)/sin(x). Starting from the left-hand side (LHS) of the identity. Multiply the single term \csc\left(x\right) by each term of the polynomial \left(\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)\right). Simplifying. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\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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