## anonymous 5 years ago can someone help with verifying a trig function?

1. anonymous

try us? lols won't know till you post the question

2. anonymous

$(\sin \theta-\cos \theta)^{2}=1-2\sin^{2} \theta \cot \theta , Verify?$

3. anonymous

i'm going to skip the theta sign so here goes sin^2 - 2sin*cos + cos^2 = 1 - 2sin^2(cos/sin) sin^2 - cos^2 = 1 1 - 2 sin*cos = 1 - 2sin(cos they are equal make sense?

4. anonymous

thank you but just give me a second to make sure i got it

5. anonymous

sure thing

6. anonymous

how did you get to sin^2 - 2sin*cos + cos^2 = 1 - 2sin^2(cos/sin)

7. anonymous

where did the 2sin come from specifically

8. anonymous

i foiled the left side of the equation and tangent is equal to sin/cos so cot is equal to cos/sin

9. anonymous

(a - b)^2 a^2 -2ab + b^2 it's foil

10. anonymous

does that make sense?

11. anonymous

i think im having trouble with the foiling

12. anonymous

umm do you know how to foil? (a - b)(a - b) a^2 - ab - ab + b^2 (sin - cos)(sin - cos) sin^2 - sin*cos - sin*cos + cos^2 sin^2 - 2sin*cos + cos^2

13. anonymous

okay thank you for yor help i see what i was doing wrong, i was foiling wrong, little rusty on the algebra

14. anonymous

no problem

15. anonymous

hey you have time for another?

16. anonymous

sure

17. anonymous

Sec^4-tan^4, what trig function is it equal to?

18. anonymous

sec is 1/cos

19. anonymous

1/cos^4 - sin^4/ cos^4 (1 - sin^4) / cos^4 cos^2 + sin^2 = 1 so cos^2 = 1 - sin^2 [(1 - sin^2)(1 + sin^2)]/ cos^4 (1 + sin^2)/ cos^2

20. anonymous

i'm not sure if you can get more simplified than that..

21. anonymous

sin^2 = 1 - cos^2 (1 + 1 - cos^2)/ cos^2 (2 - cos^2) / cos^2 2sec^2 - 1 there that's one trig function

22. anonymous

the choices are A) Sec^2 B) csc C) tan D) Sec^2+tan^2 E) sin^2 F) sin*tan

23. anonymous

the answer is D where i stopped first (1 + sin^2)/ cos^2 if you divide that out you'll get sec^2 + tan^2

24. anonymous

ohh man thanks that one was killin me lol just for my own knowledge where do you start first when you see a problem like that? like what goes through your mind first?

25. anonymous

i hate doing trig functions all i can say is something that you've probably heard 100s of times practice but seriously, the more you practice, the easier it is key hints cos^2 + sin^2 = 1 <-- super big and useful tan = sin/cos there are also the rarer ones half angle formulas

26. anonymous

just move the functions around until you see something familiar and you'll see things to cancel out your object to make it as simple as possible

27. anonymous

ok cool keep those in mind i have one question, how did you go from [(1 - sin^2)(1 + sin^2)]/ cos^4 to (1 + sin^2)/ cos^2

28. anonymous

i wrote before that line that cos^2 = 1 - sin^2 which i got from sin^2 + cos^2 = 1 see? very useful since those are equal, i canceled from top and bottom does that make sense?

29. anonymous

yes i see it now, and i see how you were left with the answer. your helping me out big time lol

30. anonymous

lol awesome ^_^

31. anonymous

alright ive got another one for you ive been trying it for a while but keep hittin dead ends, got time?

32. anonymous

go for it

33. anonymous

1/2(1+sin/cos+cos/1+sin) , what trig function is equal? Sin cos tan csc sec cot

34. anonymous

cos/1? you sure, caz that's just cos

35. anonymous

yup cos/(1+sin)

36. anonymous

oh i see you need to use parenthesis rocco, otherwise there's a lot of miss understandings

37. anonymous

ohh im sorry

38. anonymous

oh and the first part is (1+sin)/cos

39. anonymous

1/2(1+tan+cos+cot))

40. anonymous

T-T

41. anonymous

i feel quite useless....

42. anonymous

give me some time, i'm going to write this out, sorry

43. anonymous

no problem, and ure not useless dont worry about that lol

44. anonymous

rocco i have no luck for this one :x sorry! repost this one

45. anonymous

ok no prob, found another one, wanna take a crack at it, i thnk i got half of it?

46. anonymous

rofl sure

47. anonymous

ok its csc - cot = 1/ (csc + cot) verify

48. anonymous

(csc - cot)(csc + cot) = 1 csc^2 - cot^2 = 1 ^-- that's another rule you should remember

49. anonymous

ohh but can you cross the = sign when verifying?

50. anonymous

i'm not sure i understand what you mean?

51. anonymous

somewhere i heard that when you verify the = becomes like a wall that you cant cross and only work on either side to make them equal, maybe im just understanding your work wrong

52. anonymous

i don't think i've heard that rule 2 + 4 = 8 - 2 if i add 2 on to both sides (crossing?) i get 6 = 6 do you mean crossing like this?

53. anonymous

yea like that

54. anonymous

it's perfectly fine as i just shown up there LOL 6 is equal to 6 so it's fine cheers ^_^

55. anonymous

ohh i see, haha thanks youve been a big help!!!