## anonymous one year ago 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

1. freckles

try expanding the cos(a-b) part

2. anonymous

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

3. freckles

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

4. freckles

you don't know the difference identity for cosine?

5. anonymous

No. My textbook never showed or told me.

6. anonymous

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

7. 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

8. anonymous

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

9. anonymous

@freckles

10. freckles

yes?

11. anonymous

Can you help me a little better?

12. freckles

can you tell me if you applied that identity yet?

13. anonymous

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

14. freckles

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

15. freckles

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

16. anonymous

I do and yes.

17. freckles

well can you apply that identity then...

18. freckles

like can you expand cos(a-b)

19. anonymous

The expanding is the confusing part. Never done it.

20. 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?

21. anonymous

I see now.

22. freckles

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

23. freckles

and you have expanded cos(a-b)

24. anonymous

Okay. Is that all I do?

25. freckles

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

26. freckles

I actually gave a few more steps above after the expansion

27. anonymous

Okay. Thanks!

28. freckles

something about separating the fraction canceling stuff and rewriting a bit

29. freckles

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

30. freckles

or show me what you have for the numerator please

31. anonymous

Yes

32. anonymous

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

33. freckles

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

34. freckles

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

35. freckles

cos(a-b)=?

36. freckles

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37. anonymous

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

38. freckles

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39. freckles

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40. anonymous

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

41. 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)

42. anonymous

Okay. I am understanding a little more.

43. anonymous

So, 1 + cot a????

44. anonymous

@freckles

45. freckles

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

46. anonymous

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

47. anonymous

I thought it was 1

48. freckles

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

49. anonymous

I do.. Sort of.

50. freckles

then what does it equal?

51. anonymous

Tan a tan b?

52. freckles

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

53. freckles

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

54. anonymous

I meant that

55. freckles

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

56. anonymous

I am on the right track?

57. freckles

we should be done

58. freckles

so I hope so :p

59. anonymous

So, it is c ?

60. anonymous

*?

61. freckles

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

62. anonymous

Yay! Thank you, thank you!