Question

Simplify sin^2(x-1)/cos(-x)

Answer 1

@Hero

Answer 2

I know what happened now

Answer 3

You posted:
\[\frac{\sin^2(x - 1)}{-\cos(x)}\]

But what you really meant to post was
\[\frac{\sin^2(x) - 1}{\cos(-x)}\]

Answer 4

Those are two different expressions

Answer 5

ah! did i type it in wrong?!

Answer 6

The second one simplifies to one of your answer choices.

Answer 7

i'm sorry!

Answer 8

Yes, you did

Answer 9

I was a bit thrown off at first, but I assumed what you wrote was correct.

Answer 10

Well, in this case \(\sin^2x = 1 - \cos^2(x)\)

Answer 11

That should be the only hint you need.

Answer 12

\[\frac{ 1-\cos ^2\left( x-1 \right) }{ \cos \left( -x \right) }\]

Answer 13

\[\frac{ 1-\cos ^2( x)-1 }{ \cos \left( -x \right) }\]

Answer 14

Why do you keep putting the 1 in parentheses?

Answer 15

Is that what you see on your reference sheet?

Answer 16

but isn't it apart of it?

Answer 17

No, it isn't.

Answer 18

it looks like this

Answer 19

Write it out on the board what you see

Answer 20

If it has the 1 in parentheses, then it is a mistake.

Answer 21

\[\frac{ \sin ^2x-1 }{ \cos \left( -x \right) }\]

Answer 22

ahhh the sin^2x is seperate from the 1

Answer 23

ahhh

Answer 24

Yes, and you only replace the \(\sin^2(x)\) with \(1 - \cos^2(x)\)

Answer 25

1 - (-1) = 2, so would it be 2 .... cos^2(x)

Answer 26

so would it be -cos^2(x)/cos(-x)

Answer 27

Hmmm, but hang on.

Answer 28

because the problem became:

Answer 29

We know what the end result should be

Answer 30

1 - 1 = 0 like I said

Answer 31

\[\frac{ 1-\cos ^2\left( x \right)-1 }{ \cos \left( -x \right) }\]

Answer 32

Yes, that is correct now.

Answer 33

haha i'm sorry

Answer 34

so it the top cos going to be negative stil?

Answer 35

And then
\[\dfrac{-\cos^2(x)}{\cos(-x)}\] is what you should have up to this point.

Answer 36

But \(\cos(-x) = -\cos(x)\)

Answer 37

However there's still an issue somewhere.

Answer 38

Because
\[\dfrac{-\cos^2x}{\cos(-x)} = \dfrac{-\cos^2(x)}{-\cos(x)}\]

Answer 39

\[\frac{ -\cos ^2\left( x \right) }{ -\cos \left( x \right) }\]

Answer 40

If we simplify that we end up with only \(\cos(x)\) instead of \(-\cos(x)\)

Answer 41

one of the choices are cos(x)

Answer 42

I know, however, my calc is never wrong.

Answer 43

haha okay, so it shouldn't be cos(x) but -cos(x)

Answer 44

Hang on. Let me check something

Answer 45

hmm i'm trying to think of how to help but my calc is usually wrong lol

Answer 46

I have it now. In the denominator, \(\cos(-x) = \cos(x)\). So there we go.

Answer 47

So to be clear, the correct answer is \(-\cos(x)\)

Answer 48

yes, that makes sense! thank you, i think i am starting to kind of understand but its very hard stuff. I do have another one, could i open another question and you can help me with it?

Answer 49

Okay, maybe this next one will be better.

Answer 50

haha you were perfect, thank you very much!