sec^2x - 2 = tan2x

Question

sec^2x - 2 = tan2x

debbieg · Answer

is it:        $\Large \sec^2x-2=\tan^2x$

debbieg · Answer

Of        $\Large \sec^2x-2=\tan(2x)$

anonymous · Answer

Im sorry its the first one

debbieg · Answer

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 · Answer

yes solve my options are 

no solution 

pi/3

pi/4

pi/6

debbieg · Answer

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 · Answer

so is it no solutions? I tried pi/4 and that was wrong

debbieg · Answer

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 · Answer

$\Large \sec^2x-2=\tan^2x$

Substituting in the ID above:

$\Large (\tan^2x+1)-2=\tan^2x$

What next?

anonymous · Answer

subtract two from the one so 

(tan^2x-1) = tan^2x ?

debbieg · Answer

Good. what now?

anonymous · Answer

should we pass the same thing onto one side so ???


tan^2x-tan^2x= -1

debbieg · Answer

Right... which gives you what?

anonymous · Answer

pi/4 ?

debbieg · Answer

noooo....

What is the equation?

anonymous · Answer

tan^4x=-1  ??

debbieg · Answer

No.... they are like terms, so you subtract them... and you get:

0=-1

right?

anonymous · Answer

ok i get it then what else do i do?

debbieg · Answer

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 · Answer

It's just like trying to solve:

x+1=x+3

you get
1=3

which is FALSE, because there are NO solutions.

anonymous · Answer

ahhh thats why :)

anonymous · Answer

thanks i really do appreciate it.

debbieg · Answer

no problem, happy to help :)