Prove the trigonometric identity $\sec\left(2a\right)-\tan\left(2a\right)=\frac{\cos\left(a\right)-\sin\left(a\right)}{\cos\left(a\right)+\sin\left(a\right)}$

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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
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Starting from the right-hand side (RHS) of the identity

Learn how to solve factor by difference of squares problems step by step online.

$\frac{\cos\left(a\right)-\sin\left(a\right)}{\cos\left(a\right)+\sin\left(a\right)}$

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Learn how to solve factor by difference of squares problems step by step online. Prove the trigonometric identity sec(2a)-tan(2a)=(cos(a)-sin(a))/(cos(a)+sin(a)). Starting from the right-hand side (RHS) of the identity. Multiply and divide the fraction \frac{\cos\left(a\right)-\sin\left(a\right)}{\cos\left(a\right)+\sin\left(a\right)} by the conjugate of it's denominator \cos\left(a\right)+\sin\left(a\right). Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Applying the trigonometric identity: \cos\left(\theta \right)^2-\sin\left(\theta \right)^2 = \cos\left(2\theta \right).

Final answer to the problem

true

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Plotting: $true$

Main Topic: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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