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Prove the trigonometric identity $\frac{1+\sin\left(\theta\right)}{\cos\left(\theta\right)}+\frac{\cos\left(\theta\right)}{1+\sin\left(\theta\right)}=2\sec\left(\theta\right)$

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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
  • 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.

$\frac{1+\sin\left(\theta\right)}{\cos\left(\theta\right)}+\frac{\cos\left(\theta\right)}{1+\sin\left(\theta\right)}$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (1+sin(t))/cos(t)+cos(t)/(1+sin(t))=2sec(t). Starting from the left-hand side (LHS) of the identity. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Simplify the numerators.

Final answer to the problem

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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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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