Question

tan^2x + sec^2x = 1

Answer 1

What is the question

Answer 2

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

Answer 3

Give me a sec

Answer 4

What kind of question is this

Answer 5

If you multiply everything by cos^2x then you'll have sin^2x + 1 = cos^2x, which is one of the other trig identities. I'm not sure if that helps or not.

Answer 6

You have so many people on it right now

Answer 7

I dont get this problem at all. Why would I multiply it by cos ^2x?

Answer 8

Are you trying to relate all of the trig identities to eachother?

Answer 9

yeah

Answer 10

The original one is sin^2x + cos^2x = 1.
To get the other ones, you'd have to either divide by sin^2x or cos^2x.
In the case of tan^2x - sec^2x = 1, sin^2x + cos^2x = 1 was divided by cos^2x. and then set equal to 1.

Answer 11

\[\sec ^2x-\tan ^2x=1\]
adding
\[2 \sec ^2x=2\]
\[\frac{ 2 }{ \cos ^2x }=2\]
\[2 \cos ^2x=2,1+\cos 2 x=2,\cos 2x=2-1=1=\cos 2 n \pi\]
\[2x= 2 n \pi,x=n \pi, \]
where n is an integer.

Answer 12

\[\tan ^2x+\sec ^2x=1\]
it is not an identity.
the problem can be solve it or find x.

Answer 13

wait I might be wrong, so would it be sin^2x+cos^2x all divided by cos^2x?

Answer 14

No, you're not wrong. The sign doesn't match up.

Answer 15

This is so confusing :/

Answer 16

Do it!! \(\sin^{2}(x) + \cos^{2}(x) = 1\)

\(\dfrac{\sin^{2}(x)}{\cos^{2}(x)} + \dfrac{\cos^{2}(x)}{\cos^{2}(x)} = \dfrac{1}{\cos^{2}(x)}\)

\(\tan^{2}(x) + 1 = \sec^{2}(x)\)

Answer 17

All of the trig functions are related by the unit circle (which has a radius of 1). the coordinates along the unit circle are similar to regular coordinates.
The cosine value is equal to x.
The sine value is equal to y.
If you plug all those into the pythagorean theorem, then cos^2x + sin^2x = 1.
From there, you either divide by sine or cosine to get the other trig identities.
The original divided by sine is
cot^2x + 1 = csc^2x
The original divided by cosine is
tan^2x +1 = sec^2x.

Answer 18

ok i think i understand that

Answer 19

Therefore, I don't think the identity tan^2x + sec^2x = 1 can be verified.

Answer 20

ok i think i understand that

Answer 21

Because its not one of the identities.

Answer 22

Really bad language. If it's an "Identity", it CAN be verified. If it cannot be verified, it is NOT an Identity.

Answer 23

It may be true for some values.

Answer 24

Thank you. That is why I was so confused.