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Prove the trigonometric identity $\tan\left(\theta\right)\sin\left(\theta\right)+\cos\left(\theta\right)=\sec\left(\theta\right)$

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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.

$\tan\left(\theta\right)\sin\left(\theta\right)+\cos\left(\theta\right)$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity tan(t)sin(t)+cos(t)=sec(t). 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)}. Multiplying the fraction by \sin\left(\theta\right). Combine all terms into a single fraction with \cos\left(\theta\right) as common denominator.

Final answer to the problem

true

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Similar Problems Solved

Prove the identity

$\frac{1}{1-sin\left(x\right)}-\frac{1}{1+\sin\left(x\right)}=2\tan\left(x\right)sec\left(x\right)$

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

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$\frac{1+\cos2x}{\sin2x}=\cot x$

Prove the identity

$sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}$

Prove the identity

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

Prove the identity

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

Prove the identity

$\sec x-\sin x\tan x=\cos x$

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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