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is it: \(\Large \sec^2x-2=\tan^2x\)
Of \(\Large \sec^2x-2=\tan(2x)\)
Im sorry its the first one
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?
yes solve my options are no solution pi/3 pi/4 pi/6
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. :)
so is it no solutions? I tried pi/4 and that was wrong
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.... :)
\(\Large \sec^2x-2=\tan^2x\) Substituting in the ID above: \(\Large (\tan^2x+1)-2=\tan^2x\) What next?
subtract two from the one so (tan^2x-1) = tan^2x ?
Good. what now?
should we pass the same thing onto one side so ??? tan^2x-tan^2x= -1
Right... which gives you what?
noooo.... What is the equation?
No.... they are like terms, so you subtract them... and you get: 0=-1 right?
ok i get it then what else do i do?
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. :)
It's just like trying to solve: x+1=x+3 you get 1=3 which is FALSE, because there are NO solutions.
ahhh thats why :)
thanks i really do appreciate it.
no problem, happy to help :)