anonymous one year ago Show(1-tanx)/(1+tanx)^2 = cos2x?

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1. anonymous

is that cos^2(x) or cos(2x)

2. anonymous

cos(2x)

3. anonymous

4. anonymous

http://prntscr.com/86l5g2 this one

5. anonymous

turn tan in sin/cos and play around with it, tell me if u are still stuck

6. anonymous

how to settle the(1+tanx)^2 i keep cant not get the answer cos2x

7. anonymous

To me, it is not an identity. Counterexample Let test x = pi/6, the LHS = 0.1698729811 while the RHS =0.5

8. anonymous

can do full step to me? i realy no idea==

9. anonymous

to convert (1-tanx)/(1+tanx)^2 to cos2x

10. xapproachesinfinity

try to simplify (1+tanx)^2 to (sec^2x+2tanx) sec^2x+2sinx/cosx

11. xapproachesinfinity

do like dan suggested transfer tan to sin/cos that will be helpful

12. anonymous

if it is (1-tan^2x)/(1+tan^2x)^2

13. anonymous

?

14. xapproachesinfinity

hmm no i was talking about the denominator of left hand side (1+tanx)^2

15. xapproachesinfinity

manupilate that a bit more into sin and cos

16. xapproachesinfinity

then after that do the same with top too

17. anonymous

but there is the square2 there confusing me

18. xapproachesinfinity

the square you need to distribute like you do with (a+b)^2

19. anonymous

is(1+tan^4x) equal to sec^4x?

20. xapproachesinfinity

no

21. xapproachesinfinity

there is no such identity we have 1+tan^2x=sec^2x

22. xapproachesinfinity

let me start a bit $$\huge \frac{1-\tan x}{\sec^2x +2\frac{\sin x}{\cos x}}=\frac{\frac{\cos x-\sin x}{\cos x}}{\frac{1}{\cos^2x}+2\frac{\sin x}{\cos x }}$$

23. xapproachesinfinity

see if you can finish it off

24. xapproachesinfinity

you can cancel that cos that is in top and bottom

25. IrishBoy123

|dw:1440019023761:dw|

26. anonymous

|dw:1440019515190:dw|

27. xapproachesinfinity

damn why did post the wrong question lol

28. xapproachesinfinity

29. anonymous

haha sorry but i still learn to u

30. xapproachesinfinity

well you had us work the wrong thing all the way hhh but no worries

31. xapproachesinfinity

work the other way around from cos2x

32. IrishBoy123

|dw:1440019749527:dw|

33. xapproachesinfinity

cos2x=cos^2x-sin^2x

34. xapproachesinfinity

factor cos^2x to get cos^2x(1-tan^2x)

35. xapproachesinfinity

that's one step

36. xapproachesinfinity

recall that cos^2x=1/sec^2x

37. xapproachesinfinity

but again you sure it is (1+tan^2x)^2? make sure

38. xapproachesinfinity

should be only 1+tan^2x

39. anonymous

hh ya realy sure

40. anonymous

i need to proven the answer is cos2x

41. xapproachesinfinity

|dw:1440020130101:dw|

42. anonymous

yup

43. xapproachesinfinity

i got 1-tan^2x/1+tan^2x=cos^2 not square the bottom

44. xapproachesinfinity

it cannot be right the way you wrote it please make sure post the picture yo getting u all confused now hhhh

45. anonymous

but still can get the answer as cos2x jz dono the way how to do

46. xapproachesinfinity

no it can't if my result is correct that cannot be true

47. xapproachesinfinity

unless you have a different question

48. anonymous

the last picture you post is my question

49. IrishBoy123

screenshot, or url

50. IrishBoy123

51. xapproachesinfinity

please screenshot that thing man we got confused now

52. xapproachesinfinity

53. anonymous

ya this is my question as exam

54. freckles

does it say to disprove or to prove?

55. freckles

or does it just say to show?

56. xapproachesinfinity

well depends on what the question really states perhaps it want to you see whether that is an identity or not

57. xapproachesinfinity

so to answer this it is not true not an identity

58. anonymous

|dw:1440020646681:dw|

59. anonymous

if like this?

60. xapproachesinfinity

look if it is not an identity no matter what you try you won't get there haha

61. anonymous

62. IrishBoy123

|dw:1440020700278:dw|

63. anonymous

lrisboy 123 i think there is no number inn answer because cos2x is the answer jz need to prove it (1-tan^2x)/(1+tan^2x)^2 equal to cos2x

64. IrishBoy123

there should be *every * number in answer, if it was true. yes? x = 0 works. !!

65. freckles

but they already said it cannot be proven because it is not an identity @IrishBoy123 was giving a counterexample aka proving it is a false equation

66. IrishBoy123

thanks @freckles

67. freckles

if you meant $\frac{1-\tan^2(x)}{1+\tan^2(x)}=\cos(2x)$ we would have had more luck

68. freckles

because this is a true equation

69. freckles

on the left hand side's domain of course

70. anonymous

$$\dfrac{1-tan^2(x)}{(1+tan^2(x))^2}\\=\dfrac{1-tan^2(x)}{sec^4(x) }\\= \dfrac{1}{sec^4x}-\dfrac{tan^2x}{sec^4x}\\= cos^4x-cos^2xsin^2x\\=cos^2(x)(cos^2(x)-sin^2(x) )= cos^2(x) (cos(2x))$$ No way for you to get cos (2x) only.