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

Step-by-step Solution

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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 RHS (right-hand side)
  • Prove from LHS (left-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 right-hand side (RHS) of the identity

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

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

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)+cos(x)=(1+tan(x))/sec(x). Starting from the right-hand side (RHS) of the identity. Expand the fraction \frac{1+\tan\left(x\right)}{\sec\left(x\right)} into 2 simpler fractions with common denominator \sec\left(x\right). Applying the trigonometric identity: \displaystyle\frac{1}{\sec(\theta)}=\cos(\theta). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}.

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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