Question

Which of the following are identities? CHECK ALL THAT APPLY.

Answer 1

c

Answer 2

@shulee Explain her.

Answer 3

is it just c?

Answer 4

i thought maybe D as well?

Answer 5

No...it's none of them.

Answer 6

wha

Answer 7

i think c is correct?

Answer 8

Totally...You want the ansur right? it's none of them.

Answer 9

but that's not a choice lol

Answer 10

@isabel_xxvi
Do you know the very basic identity
\(sin^2 x + \cos^2x = 1\) ?

Answer 11

well, I guess if you choose none, is an implicit choice =)

Answer 12

yes I do know

Answer 13

@isabel_xxvi
Ok. Look closely at choice C.
Can you change the basic identity I wrote to make it look like C.?

Answer 14

ohh i thought you couldnt switch around stuff with identities

Answer 15

so would it be A as well?

Answer 16

When you prove an identity, it's normal to keep the sides separate, and work on one side or the other side, or both sides to make both sides look the same.
Here we are just trying to see if the identity is true.

Answer 17

So far, we know that C is true.

Answer 18

I think A is?

Answer 19

a is also true?

Answer 20

Ok, let's look at A.
\(\cot^2 x = \csc^2 x - 1\)

Answer 21

Start with this:

\(sin^2 x + \cos^2 x = 1\)

Change to this:

\(\cos^2 x = 1 - sin^2 x\)

Divide both sides by \(\sin^2 x\).
What do you get?

Answer 22

i thought 1 + cot^2x = csc^2 x
is already an identity?

Answer 23

so I thought I'd just switch the 1like I did for C

Answer 24

Yes, you are correct. If you remember that identity, then it's less work. A is also an identity.

Answer 25

Ah thanks!

Answer 26

Now look at D. The answer is obvious that it is not an identity.

Answer 27

Yeap I see

Answer 28

The same goes for B. It isn't an identity.

Answer 29

So like can you distribute? Say (cotx + cscx)^2