Answered

Determine the correct order of steps.

\begin{tabular}{|c|c|}
\hline
Step 1 & [tex]$\tan (2x) = \frac{\frac{2 \sin (x)}{\cos (x)}}{1-\frac{\sin^2 (x)}{\cos^2 (x)}}$[/tex] \\
\hline
Step 2 & [tex]$\tan (2x) = \frac{2 \tan (x)}{1 - \tan^2 (x)}$[/tex] \\
\hline
Step 3 & [tex]$\tan (2x) = \frac{2 \sin (x) \cos (x)}{\cos^2 (x) - \sin^2 (x)}$[/tex] \\
\hline
Step 4 & [tex]$\tan (2x) = \frac{\sin (2x)}{\cos (2x)}$[/tex] \\
\hline
\end{tabular}

A. 4, 3, 5, 1, 2

B. 4, 5, 3, 1, 2

C. 3, 4, 5, 1, 2

D. 3, 4, 1, 5, 2



Answer :

GinnyAnswer
Sure, let's break down the steps and their correct order:

To express [tex]\(\tan(2x)\)[/tex] in terms of trigonometric functions of [tex]\(x\)[/tex], we start from different trigonometric identities and rearrange them logically. Let's identify the correct order of steps:

1. Step 3: Start with [tex]\(\tan(2x)\)[/tex], we want to express [tex]\(\tan(2x)\)[/tex] in terms of sine and cosine:
[tex]\[ \tan(2x) = \frac{2 \sin(x) \cos(x)}{\cos^2(x) - \sin^2(x)} \][/tex]

2. Step 4: Simplify the expression using the identity [tex]\(\sin(2x) = 2\sin(x)\cos(x)\)[/tex] and [tex]\(\cos(2x) = \cos^2(x) - \sin^2(x)\)[/tex]:
[tex]\[ \tan(2x) = \frac{\sin(2x)}{\cos(2x)} \][/tex]

3. Step 1: Recognize that [tex]\(\tan(x) = \frac{\sin(x)}{\cos(x)}\)[/tex] and substitute [tex]\(\sin(x)\)[/tex] and [tex]\(\cos(x)\)[/tex] back:
[tex]\[ \tan(2x) = \frac{\frac{2\sin(x)}{\cos(x)}}{1 - \frac{\sin^2(x)}{\cos^2(x)}} \][/tex]

4. Step 2: Simplify using the identity [tex]\(\tan(x) = \frac{\sin(x)}{\cos(x)}\)[/tex]:
[tex]\[ \tan(2x) = \frac{2\tan(x)}{1 - \tan^2(x)} \][/tex]

The detailed, step-by-step solution results in the correct order: [tex]\(3, 4, 1, 5, 2\)[/tex].

So, the correct selection is:
[tex]\[4, 5, 3, 1, 2\][/tex]

Other Questions