Question

How do you solve -tan^2x + sec^2x = 1?

Answer 1

` sec²x = 1 + tan²x ` is the rule, so if you add tan²x to both sides of your equation, then you are going to get that identity I wrote in grey.

You can multiply everything times cos²x and you are going to get
` 1 = cos²x + sin²x `

Answer 2

Your expression is an identity for all real values of x.

Answer 3

Wait, I'm still not sure I fully understand.. How would it be solved so that it would equal the same thing on both sides? I'm trying to help my friend out with this problem and am a tad puzzled by it still. Isn't the answer supposed to end up being 1 = 1 ?

Answer 4

It says it's supposed to be verified?

Answer 5

You can either add tan²x to both sides of your expression,
and you will get an identity - ` sec²x = 1 + tan²x `.
Or you can multiply everything in your expression and you
will also get an identity - ` 1 = cos²x + sin²x `.

Answer 6

Does 1 + tan^2x = sec^2x? Like, once I add tan^2x to both sides.. It should cancel out or? I'm sorry I'm just really confused by this and am trying to figure out how it works.. How exactly is it verified if you don't mind me asking?

Answer 7

So, to solve it it would be
-tan^2x + sec^2x = 1
sec^2x = 1 + tan^2x
sec^2x = sec^2x?

Answer 8

read what I said. I am saying "blank", and you are re-asking "blank ? "

Answer 9

I just wanted to be sure that that would be how it's solved. I'm assuming it's correct then? I only wanted to be completely positive that I would be giving the right work for the equation.

Answer 10

Yes, what I said is 100% correct. I guarantee, and I am positive .

Answer 11

Thank you.