## lilsis76 3 years ago Prove the identites are Equal Sin A - cos A / sin A + cos A - sin A / cos A = 2 - sec A csc A

1. lilsis76

|dw:1349291754923:dw| @hartnn this is the other problem.

2. hartnn

write cos A - sin A as - (sin A-cos A)

3. lilsis76

|dw:1349292009958:dw|

4. hartnn

i asked u to write cos A - sin A as - (sin A-cos A) u have written cos A - sin A as - (cos A + sin A) ..... -.- ....

5. lilsis76

oh. haha. im sorry im very bad at this. im more of a visual learner. just a moment let me fix this.

6. lilsis76

wait, i just realized, were talking about the far left fraction right?

7. hartnn

middle.

8. lilsis76

oka. let me try now

9. lilsis76

|dw:1349292496553:dw|

10. hartnn

i asked u to write cos A - sin A as - (sin A-cos A) u have written cos A - sin A as - (sin A +cos A) ..... -.- ....

11. lilsis76

but how is that possible that its a - cos A ? I dont see it

12. hartnn

- (sin A-cos A) = -sin A -(-cos A) = -sin A +cos A = cos A -sin A

13. lilsis76

|dw:1349292833969:dw|

14. hartnn

ok , lets forget everything, lets go another way. can u separate out the denominator ?

15. hartnn

like (a+b)/c = a/c + b/ c

16. lilsis76

i think i can, but it would be in 4 sections right? like sin A / Sin A - cos A/sinA + cos A/cos A -sinA/cos A

17. hartnn

absolutely correct! whats sin A/ sin A =? and cos A/cos A = ?

18. lilsis76

there going to equal 1

19. hartnn

so u got 2 right ?

20. lilsis76

what? well if u add them 1 + 1 = that makes 2

21. hartnn

yes. now u are left with -cos A/sinA -sinA/cos A cross multiply again, same as previous problem

22. lilsis76

|dw:1349293671738:dw|

23. hartnn

which is ?

24. lilsis76

which is 1

25. hartnn

-(sin^2x + cos^2 x) = -1

26. lilsis76

oh shoot. thats right... okay because it was a negative the answer will be negative too.

27. lilsis76

okay i got the same answer too

28. hartnn

what was left in the denominator

29. lilsis76

|dw:1349293889401:dw|

30. lilsis76

Okay this is what i have so far. I like to put things in steps.

31. hartnn

|dw:1349294146174:dw| see this.

32. hartnn

makes sense ?

33. lilsis76

ya i see it, i under stand it but just forgot where the 2 came from. it came from the 2 fractions that crossed each other out right?

34. hartnn

it came from sinx/sin x + cosx / cos x = 1+1 = 2

35. lilsis76

okay, ya thats what i thought :)

36. lilsis76

now how can we get rid of that - 1 ?

37. hartnn

|dw:1349294542963:dw| what is 1/sin a and 1/ cos a ?

38. lilsis76

the 1/ sin a = the inverse of cos. that is csc and 1/ cos a = is the inverse of sine sec

39. hartnn

|dw:1349294713780:dw| got it ?

40. lilsis76

i got it..............man WHAT THE HEY?! why is this so complicating?!

41. lilsis76

do u have any advice for me to kind of remember what to do. Because I know what the inverse fractions look like and everything I just get stuck all the time.

42. hartnn

3 tips: 1. practice. 2. more practice. 3. more and more practice. want 4th ? :P

43. lilsis76

really?!......I try doing more homework problems as practice and i get more confused. then i go to tutoring at school. ugH?! math hates my brain

44. hartnn

have patience, you will understand someday. else i will be there to help u.

45. lilsis76

okay then. Thank you for helping me out. Im going to work on english. Have a good day.

46. hartnn

think positive, think u like math. u also have a good day, i will have good night :)

47. lilsis76

|dw:1349295088469:dw|

48. hartnn

|dw:1349295140875:dw|