Question

Simplify 1-sin^2x/cosx

Answer 1

HINT :
\[\large \rm \sin^2x + \cos^2x = 1\]

Answer 2

I know that's an identity but I don't know how to get it like that

Answer 3

you do not want to change your question to look like the identity. you change the identity to look like your question

Answer 4

So I have 1-sin^2x = cos^2x now...

Answer 5

can i clarify something first?

Answer 6

is this the original equation?
\[\frac{ 1-\sin(x)^2 }{ \cos(x) }\]

Answer 7

Yes

Answer 8

okay good

Answer 9

so what you just did was right!

Answer 10

now that you know that 1- sin(x)^2 is the same as cos(x)^2 what do you want to do? i see something similar in the equation!

Answer 11

It's similar to the sin^2x+cos^2x=1 identity?

Answer 12

wait wait!

Answer 13

remember when you said you got\[1-\sin(x)^2 = \cos(x)^2\]

Answer 14

Yes..what should I do after that?

Answer 15

where do you see\[1-\sin(x)^2\]

Answer 16

lets remember your original equation\[\frac{ 1-\sin(x)^2 }{ \cos(x) }\]

Answer 17

hint: you can replace something with the identity you have found, \(\cos^2 (x) = 1-\sin^2 (x)\)

Answer 18

I see 1-sin^2x on top

Answer 19

great! do substitution!

Answer 20

when you replace \(1-\sin^2 (x)\) with \(\cos^2 (x)\) what do you get?

Answer 21

Cosx?

Answer 22

yes :)

Answer 23

\[\frac{\cos^2(x)}{\cos(x)} = \cos(x) \implies \frac{x^2}{x} = x\]

Answer 24

Great! But the only thing I'm confused on is why we replaced 1-sin^2x with cos^2x

Answer 25

Because the identity whispered it into your ear and told you to do so.

Answer 26

Hahaha

Answer 27

Jk, we found he infamous identity \[\sin^2(x) +\cos^2(x) = 1\] and because we were already given \(\color{red}{1-\sin^2(x)}\) in our problem, we were able to use this identity to find out what it was equal to:\[\color{blue}{cos^2(x)} = \color{red}{1-sin^2(x)}\] so we just substituted it in.

You can do that with identities, it's legit :P

Answer 28

Are you good? Do you understand? :o

Answer 29

Thanks! It's 1:36 AM here so I'm kinda on the struggle bus. But yeah you guys helped a lot! :)

Answer 30

Good luck :)

Answer 31

california i bet? same time here