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Prove the trigonometric identity $\frac{\cos\left(\theta\right)\left(\tan\left(\theta\right)+\sin\left(\theta\right)\right)}{\sin\left(\theta\right)}=1+\cos\left(\theta\right)$

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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

$\frac{\cos\left(\theta\right)\left(\tan\left(\theta\right)+\sin\left(\theta\right)\right)}{\sin\left(\theta\right)}$

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

$\frac{\cos\left(\theta\right)\left(\tan\left(\theta\right)+\sin\left(\theta\right)\right)}{\sin\left(\theta\right)}$

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

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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