I need complete help..
Complete the identity.
Cos(a -b)/cos a cos b
A. 1 + cot a cot b
B. Tan a tan b + cot b
C. 1 + tan a tan b
D. 1 + cot a tan b

- anonymous

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- freckles

try expanding the cos(a-b) part

- anonymous

How? I look at my textbook, but it isn't helping me understand more.

- freckles

then separate the fraction after the expansion
do some canceling
and finally just a little rewriting

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## More answers

- freckles

you don't know the difference identity for cosine?

- anonymous

No. My textbook never showed or told me.

- anonymous

It just gives me problems to do and then I take my test.

- freckles

sin(x-y)=sin(x)cos(y)-sin(y)cos(x)
sin(x+y)=sin(x)cos(y)+sin(y)cos(x)
cos(x+y)=cos(x)cos(y)-sin(x)sin(y)
cos(x-y)=cos(x)cos(y)+sin(x)sin(y)
so you never seen these identities?
that is odd

- anonymous

Correct. I am working hard to learn.. But I am confused.

- anonymous

@freckles

- freckles

yes?

- anonymous

Can you help me a little better?

- freckles

can you tell me if you applied that identity yet?

- anonymous

Like, I am confused. I have done some sins, cos, and tans but not like this.

- freckles

do you see the cos(a-b) on top?

- freckles

do any of the identities I mentioned look like this on the left hand side?

- anonymous

I do and yes.

- freckles

well can you apply that identity then...

- freckles

like can you expand cos(a-b)

- anonymous

The expanding is the confusing part. Never done it.

- freckles

so you don't see how cos(x-y) looks exactly like cos(a-b)
except in the place of x we have a and in the place of y we have b?

- anonymous

I see now.

- freckles

replace the x and y on the right hand side with a and b respectively

- freckles

and you have expanded cos(a-b)

- anonymous

Okay. Is that all I do?

- freckles

to expand cos(a-b) yes
for the question you have asked here at the top, no

- freckles

I actually gave a few more steps above after the expansion

- anonymous

Okay. Thanks!

- freckles

something about separating the fraction
canceling stuff
and rewriting a bit

- freckles

can you show me what you have after rewriting \[\frac{\cos(a-b)}{\cos(a)\cos(b)}\]

- freckles

or show me what you have for the numerator please

- anonymous

Yes

- anonymous

Cos(x-y)= cos(x) cos (y)
I am still somewhat confused

- freckles

ok well it looks like you didn't use the identity I mentioned above

- freckles

cos(x-y)=cos(x)cos(y)+sin(x)sin(y)

- freckles

cos(a-b)=?

- freckles

|dw:1444190564321:dw|

- anonymous

Uhhh, ??? Sorry.. I have no clue. I have never done a problem like this.
Cos(x-y)

- freckles

|dw:1444190659448:dw|

- freckles

|dw:1444190692534:dw|

- anonymous

Cos(x-y)= cos(x)cos(y) + sin(x)sin(y)

- freckles

\[\frac{\cos(a-b)}{\cos(a)\cos(b)}=\frac{\cos(a)\cos(b)+\sin(a)\sin(b)}{\cos(a)\cos(b)}\]
write as two fractions (separate the fraction)

- anonymous

Okay. I am understanding a little more.

- anonymous

So, 1 + cot a????

- anonymous

@freckles

- freckles

\[\frac{\cos(a) \cos(b)}{\cos(a) \cos(b)}=1\]
and
\[\frac{\sin(a) \sin(b)}{\cos(a) \cos(b)}=\frac{\sin(a)}{\cos(a)} \frac{\sin(b)}{\cos(b)}=...?\]

- anonymous

It equals... I have no clue. I am trying.

- anonymous

I thought it was 1

- freckles

so you don't know what tan(x) equals in terms of sin(x) and cos(x)?

- anonymous

I do.. Sort of.

- freckles

then what does it equal?

- anonymous

Tan a tan b?

- freckles

tan(x)=tan(a)tan(b)?

- freckles

or did you mean sin(a)/cos(a)=tan(a)
and sin(b)/cos(b)=tan(b)?

- anonymous

I meant that

- freckles

ok great \[\frac{\cos(a) \cos(b)}{\cos(a) \cos(b)}=1\]
while \[\frac{\sin(a) \sin(b)}{\cos(a) \cos(b)}=\frac{\sin(a)}{\cos(a)} \frac{\sin(b)}{\cos(b)}=\tan(a) \tan(b)\]

- anonymous

I am on the right track?

- freckles

we should be done

- freckles

so I hope so :p

- anonymous

So, it is c
?

- anonymous

*?

- freckles

yes that is what we got 1+tan(a)tan(b)

- anonymous

Yay! Thank you, thank you!

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