simplify the following expression for the given value of x. assume the …
$2\tan\theta$
Aufgabe
simplify the following expression for the given value of x. assume the angle \\(\\theta\\) is acute. \\(\\sqrt{x^2 - 4}\\) if \\(x = -2\\sec \\theta\\)
Lösungsschritte
-
Understand the question
simplify the following expression for the given value of x. assume the angle \\(\\theta\\) is acute. \\(\\sqrt{x^2 - 4}\\) if \\(x = -2\\sec \\theta\\)
-
Explanation
Step1: Substitute $x=-2\sec\theta$
$$\sqrt{(-2\sec\theta)^2 - 4}$$
Step2: Simplify the squared term
$$\sqrt{4\sec^2\theta - 4}$$
Step3: Factor out the common term
$$\sqrt{4(\sec^2\theta - 1)}$$
Step4: Use trigonometric identity $\sec^2\theta-1=\tan^2\theta$
$$\sqrt{4\tan^2\theta}$$
Step5: Simplify the square root
$$2|\tan\theta|$$
Step6: Use acute $\theta$ property ($\tan\theta>0$)
$$2\tan\theta$$
-
Final answer
$2\tan\theta$
Antwort
Explanation
Step1: Substitute $x=-2\sec\theta$
$$\sqrt{(-2\sec\theta)^2 - 4}$$
Step2: Simplify the squared term
$$\sqrt{4\sec^2\theta - 4}$$
Step3: Factor out the common term
$$\sqrt{4(\sec^2\theta - 1)}$$
Step4: Use trigonometric identity $\sec^2\theta-1=\tan^2\theta$
$$\sqrt{4\tan^2\theta}$$
Step5: Simplify the square root
$$2|\tan\theta|$$
Step6: Use acute $\theta$ property ($\tan\theta>0$)
$$2\tan\theta$$
Answer
$2\tan\theta$
Question Image
Click to enlargeQuestion Analysis
Subject
unspecified
Sub Subject
unspecified
Education Level
not specified
Difficulty
unspecified
Question Type
calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-07T17:05:13
OCR Text
Show OCR extraction
simplify the following expression for the given value of x. assume the angle \\(\\theta\\) is acute. \\(\\sqrt{x^2 - 4}\\) if \\(x = -2\\sec \\theta\\)
Verwandte Themen
Ähnliche Fragen
-
What areas/contient/countries do they explore
Wait, who are we talking about? I think I might have missed the first part of the conversation! Are you thinking of a specific group of explorers, a show, or maybe a game? Fill me…
-
That was perfect, but I can’t copy it so I could paste it
Oh, I got you! Here it is so you can copy and paste it easily: Hey Dad, can I skip tomorrow just this one day? Since the girls got to stay home and leave early a couple of times l…
-
Yes thank you
You're so welcome! I'm glad we could get that all squared away. It sounds like a really solid piece of writing now that you've got all those specific examples in there. If you nee…
-
Hi
Hey! How's it going?
-
Can you remind me what we covered? 🧠
Wait, did we actually talk about something specific? I feel like we just started hanging out! My brain might be a little foggy, but I don't think we've dove into anything deep yet…
-
Yes I am thank you I’ll talk to you later for any upcoming assignments …
No problem at all! I'm glad we got it to a place you liked. Good luck with the poem in class—I'm sure it'll go over great. Catch ya later! Feel free to reach out whenever you're b…
-
I’ll call it a day
\( x = \frac{4}{3} \) ### Turn 2 Answer # Knowledge Points: - Solving linear equations with one variable. - Using inverse operations (multiplication, subtraction, division) to iso…
-
18. a group of friends wants to go to the amusement park. they have $35…
The equation is \( 6 + 29.25x = 357 \), and the number of people \( x = 12 \).
Sovi AI iOS
Offizielle Website: mysovi.ai. Frage-Seiten laufen auf question-banks.mysovi.ai. Die iOS-App ist im Apple App Store verfügbar.
Im App Store laden Kategorie: Algebra