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

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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
  • Load more...
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1

Starting from the left-hand side (LHS) of the identity

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

$\frac{1+\csc\left(x\right)}{\sec\left(x\right)}-\cot\left(x\right)$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (1+csc(x))/sec(x)-cot(x)=cos(x). Starting from the left-hand side (LHS) of the identity. Combine all terms into a single fraction with \sec\left(x\right) as common denominator. Simplify -\cot\left(x\right)\sec\left(x\right) by applying trigonometric identities. Cancel like terms \csc\left(x\right) and -\csc\left(x\right).

Final answer to the problem

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Similar Problems Solved

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$sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}$

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

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$\frac{1-sin\left(x\right)}{cos\left(x\right)}=\frac{cos\left(x\right)}{1+sin\left(x\right)}$

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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