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

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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Starting from the left-hand side (LHS) of the identity

$\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)$

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$\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)$

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Learn how to solve problems step by step online. Prove the trigonometric identity sec(x)-tan(x)sin(x)=1/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)}. Multiplying the fraction by \sin\left(x\right). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.

Final answer to the problem

true

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Plotting: $true$

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