Solve the following trig equation. Be sure to write all of your solutions in a comma-separated list with no spaces. Where possible, your answers should be fully condensed. sec? x = 2 tan? x
Solve the following trig equation. Be sure to write all of your solutions in a comma-separated list with no spaces. Where possible, your answers should be fully condensed. sec? x = 2 tan? x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I got these for solutions, but symbolab (second image) got different answers. Did I do the question right? I can't find anything wrong with the way I did it, I think I'm missing something.
![Solve the following trig equation. Be sure to write
all of your solutions in a comma-separated list
with no spaces. Where possible, your answers
should be fully condensed.
sec^2(x)=2tan^2(x)
sec? x = 2 tan² x
using
1+tan^2(x)=sec^2(x),
+ Tn, + an
31
+ πη
4
1+tan^2(x)=2tan^2(x)
1=2tan^2(x)-tan^2(x}
1=tan^2(x)
tan(x)=+-1
tan(x)=1
pi/4
pi/4+pin
tan(x)=-1 3pi/4+pin
x=3pi/4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa03a5d2e-f1dd-48ec-8f8c-fb7a6a6d8d6c%2F2e652f22-d292-49e4-ab54-0ea76476aade%2Fkrau0fj_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the following trig equation. Be sure to write
all of your solutions in a comma-separated list
with no spaces. Where possible, your answers
should be fully condensed.
sec^2(x)=2tan^2(x)
sec? x = 2 tan² x
using
1+tan^2(x)=sec^2(x),
+ Tn, + an
31
+ πη
4
1+tan^2(x)=2tan^2(x)
1=2tan^2(x)-tan^2(x}
1=tan^2(x)
tan(x)=+-1
tan(x)=1
pi/4
pi/4+pin
tan(x)=-1 3pi/4+pin
x=3pi/4
![Go
sec x= 2tanx
Sy
Graph » Examples »
Relate
Solution
Keep Practicing >
Show Steps
sec (x) = 2tan (x) :
3% + 2nn, x =
+ 2nn, x = + 2nn, x =
4
(Degrees:
X=
+ 2nn
Steps
sec" (x) = 2tan (x)
Subtract 2tan (x) from both sides
sec (x) – 2tan? (x) = 0
Show Steps
sec (x) – 2tan (x): (sec(x) + v7 tan(x))(sec(x) – v7 tan(x))
(sec(x) + v7 tan(x)(sec(x) – v7 tan (x)) = 0
Solving each part separately
sec(x) + v2 tan(x) = 0
or sec(x) – v7 tan(x) = 0
Show Steps
sec (x) + v7 tan(x) = 0 :
= 31 + 2nn, x=
+ 2nn
Show Steps O
sec (x) – v7 tan(x) =0 :
x=+ 2nn, x= 3 + 2nn
Combine all the solutions
= + 2an, x= * + 2nn, x= + 2nn, x=
+ 2nn
X=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa03a5d2e-f1dd-48ec-8f8c-fb7a6a6d8d6c%2F2e652f22-d292-49e4-ab54-0ea76476aade%2F99ljnf8_processed.png&w=3840&q=75)
Transcribed Image Text:Go
sec x= 2tanx
Sy
Graph » Examples »
Relate
Solution
Keep Practicing >
Show Steps
sec (x) = 2tan (x) :
3% + 2nn, x =
+ 2nn, x = + 2nn, x =
4
(Degrees:
X=
+ 2nn
Steps
sec" (x) = 2tan (x)
Subtract 2tan (x) from both sides
sec (x) – 2tan? (x) = 0
Show Steps
sec (x) – 2tan (x): (sec(x) + v7 tan(x))(sec(x) – v7 tan(x))
(sec(x) + v7 tan(x)(sec(x) – v7 tan (x)) = 0
Solving each part separately
sec(x) + v2 tan(x) = 0
or sec(x) – v7 tan(x) = 0
Show Steps
sec (x) + v7 tan(x) = 0 :
= 31 + 2nn, x=
+ 2nn
Show Steps O
sec (x) – v7 tan(x) =0 :
x=+ 2nn, x= 3 + 2nn
Combine all the solutions
= + 2an, x= * + 2nn, x= + 2nn, x=
+ 2nn
X=
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