anonymous
  • anonymous
sec^2x - 2 = tan2x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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DebbieG
  • DebbieG
is it: \(\Large \sec^2x-2=\tan^2x\)
DebbieG
  • DebbieG
Of \(\Large \sec^2x-2=\tan(2x)\)
anonymous
  • anonymous
Im sorry its the first one

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DebbieG
  • DebbieG
are you supposed to solve the equation? Because I first assumed you want to prove an ID, but I'm pretty sure that's NOT an ID, lol... so I'm guessing solve?
anonymous
  • anonymous
yes solve my options are no solution pi/3 pi/4 pi/6
DebbieG
  • DebbieG
Well, if you use the ID: \(\Large \tan^2x+1=\sec^2x\) And sub that into the equation on the left hand side, then you get an equation with just \(\tan^2x\). From that you should be able to see pretty quickly what, if any, solutions you get. :)
anonymous
  • anonymous
so is it no solutions? I tried pi/4 and that was wrong
DebbieG
  • DebbieG
Heh... well, before I answer your question, did you follow the process to try to SOLVE it? :) I understand that when you have a mult choice question of this type, it is expedient to try the choices until you figure out which one "works". But that doesn't really teach you anything about the concept of solving this equation, kwim? so I'd rather see your process of trying to solve.... :)
DebbieG
  • DebbieG
\(\Large \sec^2x-2=\tan^2x\) Substituting in the ID above: \(\Large (\tan^2x+1)-2=\tan^2x\) What next?
anonymous
  • anonymous
subtract two from the one so (tan^2x-1) = tan^2x ?
DebbieG
  • DebbieG
Good. what now?
anonymous
  • anonymous
should we pass the same thing onto one side so ??? tan^2x-tan^2x= -1
DebbieG
  • DebbieG
Right... which gives you what?
anonymous
  • anonymous
pi/4 ?
DebbieG
  • DebbieG
noooo.... What is the equation?
anonymous
  • anonymous
tan^4x=-1 ??
DebbieG
  • DebbieG
No.... they are like terms, so you subtract them... and you get: 0=-1 right?
anonymous
  • anonymous
ok i get it then what else do i do?
DebbieG
  • DebbieG
I'm sure that was throwing you off..... but you see, that's EXACTLY what happens when you solve an "inconsistent equation" - which is an equation that has NO solutions. :)
DebbieG
  • DebbieG
It's just like trying to solve: x+1=x+3 you get 1=3 which is FALSE, because there are NO solutions.
anonymous
  • anonymous
ahhh thats why :)
anonymous
  • anonymous
thanks i really do appreciate it.
DebbieG
  • DebbieG
no problem, happy to help :)

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