Question

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

Answer 1

try expanding the cos(a-b) part

Answer 2

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

Answer 3

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

Answer 4

you don't know the difference identity for cosine?

Answer 5

No. My textbook never showed or told me.

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

@freckles

Answer 10

yes?

Answer 11

Can you help me a little better?

Answer 12

can you tell me if you applied that identity yet?

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

I do and yes.

Answer 17

well can you apply that identity then...

Answer 18

like can you expand cos(a-b)

Answer 19

The expanding is the confusing part. Never done it.

Answer 20

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?

Answer 21

I see now.

Answer 22

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

Answer 23

and you have expanded cos(a-b)

Answer 24

Okay. Is that all I do?

Answer 25

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

Answer 26

I actually gave a few more steps above after the expansion

Answer 27

Okay. Thanks!

Answer 28

something about separating the fraction
canceling stuff
and rewriting a bit

Answer 29

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

Answer 30

or show me what you have for the numerator please

Answer 31

Yes

Answer 32

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

I am still somewhat confused

Answer 33

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

Answer 34

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

Answer 35

cos(a-b)=?

Answer 36

Uhhh, ??? Sorry.. I have no clue. I have never done a problem like this.

Cos(x-y)