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Analyze this derivation of the tangent double angle identity. tan(2x) = tan (x + x) Equals StartFraction tangent (x) + tangent (x) Over 1 minus tangent (x) tangent (x) EndFraction Equals StartFraction 2 tangent (x) Over 1 minus tangent squared (x) EndFraction Choose the justification for each step. Step 1: . Step 2: . Step 3: .

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MrRoyal

The derivation steps and the reasons are:

  • [tex]\tan(2x) = \tan(x+x)[/tex] -------- Addition
  • [tex]\tan(2x) = \frac{\tan(x) + \tan(x)}{1 - \tan(x) \tan(x)}[/tex] --------- Tangent sum identity
  • [tex]\tan(2x) = \frac{\tan(x) + \tan(x)}{1 - \tan^2(x)}[/tex] ------- Simplify

What is the tangent sum identity?

The tangent sum identity states that:

[tex]\tan(a + b) = \frac{\tan(a) + \tan(b)}{1 - \tan(a) \tan(b)}[/tex]

To determine the derivation of tan(2x), we make use of the following steps.

Rewrite 2x as the addition of x and x.

So, we have:

[tex]\tan(2x) = \tan(x+x)[/tex] --- step 1

Next, we apply the tangent sum identity.

Recall that:

[tex]\tan(a + b) = \frac{\tan(a) + \tan(b)}{1 - \tan(a) \tan(b)}[/tex]

Substitute x for a and b.

So, we have:

[tex]\tan(2x) = \frac{\tan(x) + \tan(x)}{1 - \tan(x) \tan(x)}[/tex] ---- step 2

Simplify the denominator

[tex]\tan(2x) = \frac{\tan(x) + \tan(x)}{1 - \tan^2(x)}[/tex]

Hence, the result of the derivation is [tex]\tan(2x) = \frac{\tan(x) + \tan(x)}{1 - \tan^2(x)}[/tex]

Read more about trigonometric identity at:

https://brainly.com/question/7331447

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