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Prove the trigonometric identity $\cos\left(y\right)\frac{\csc\left(y\right)}{\cot\left(y\right)}=1$

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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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1

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

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

$\cos\left(y\right)\frac{\csc\left(y\right)}{\cot\left(y\right)}$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity cos(y)csc(y)/cot(y)=1. Starting from the left-hand side (LHS) of the identity. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Simplify the fraction \frac{\frac{1}{\sin\left(y\right)}}{\frac{\cos\left(y\right)}{\sin\left(y\right)}}.

Final answer to the problem

true

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Similar Problems Solved

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

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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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