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

Step-by-step 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

$\tan\left(x\right)+\frac{\cos\left(x\right)}{1+\sin\left(x\right)}$
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Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{\sin\left(x\right)}{\cos\left(x\right)}+\frac{\cos\left(x\right)}{1+\sin\left(x\right)}$
Why is tan(x) = sin(x)/cos(x) ?

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

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Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)+cos(x)/(1+sin(x))=sec(x). Starting from the left-hand side (LHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. 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.

Final answer to the problem

true

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Function Plot

Plotting: $true$

Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.

Used Formulas

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