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anonymous

  • one year ago

Show(1-tanx)/(1+tanx)^2 = cos2x?

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  1. anonymous
    • one year ago
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    is that cos^2(x) or cos(2x)

  2. anonymous
    • one year ago
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    cos(2x)

  3. anonymous
    • one year ago
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    okay start with the trig identiy for cos(2x)

  4. anonymous
    • one year ago
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    http://prntscr.com/86l5g2 this one

  5. anonymous
    • one year ago
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    turn tan in sin/cos and play around with it, tell me if u are still stuck

  6. anonymous
    • one year ago
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    how to settle the(1+tanx)^2 i keep cant not get the answer cos2x

  7. anonymous
    • one year ago
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    To me, it is not an identity. Counterexample Let test x = pi/6, the LHS = 0.1698729811 while the RHS =0.5

  8. anonymous
    • one year ago
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    can do full step to me? i realy no idea==

  9. anonymous
    • one year ago
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    to convert (1-tanx)/(1+tanx)^2 to cos2x

  10. xapproachesinfinity
    • one year ago
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    try to simplify (1+tanx)^2 to (sec^2x+2tanx) sec^2x+2sinx/cosx

  11. xapproachesinfinity
    • one year ago
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    do like dan suggested transfer tan to sin/cos that will be helpful

  12. anonymous
    • one year ago
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    if it is (1-tan^2x)/(1+tan^2x)^2

  13. anonymous
    • one year ago
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    ?

  14. xapproachesinfinity
    • one year ago
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    hmm no i was talking about the denominator of left hand side (1+tanx)^2

  15. xapproachesinfinity
    • one year ago
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    manupilate that a bit more into sin and cos

  16. xapproachesinfinity
    • one year ago
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    then after that do the same with top too

  17. anonymous
    • one year ago
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    but there is the square2 there confusing me

  18. xapproachesinfinity
    • one year ago
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    the square you need to distribute like you do with (a+b)^2

  19. anonymous
    • one year ago
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    is(1+tan^4x) equal to sec^4x?

  20. xapproachesinfinity
    • one year ago
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    no

  21. xapproachesinfinity
    • one year ago
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    there is no such identity we have 1+tan^2x=sec^2x

  22. xapproachesinfinity
    • one year ago
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    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
    • one year ago
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    see if you can finish it off

  24. xapproachesinfinity
    • one year ago
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    you can cancel that cos that is in top and bottom

  25. IrishBoy123
    • one year ago
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    |dw:1440019023761:dw|

  26. anonymous
    • one year ago
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    |dw:1440019515190:dw|

  27. xapproachesinfinity
    • one year ago
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    damn why did post the wrong question lol

  28. xapproachesinfinity
    • one year ago
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    i was wondering why your talking about 1-tan^2x in a reply so that was the question

  29. anonymous
    • one year ago
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    haha sorry but i still learn to u

  30. xapproachesinfinity
    • one year ago
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    well you had us work the wrong thing all the way hhh but no worries

  31. xapproachesinfinity
    • one year ago
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    work the other way around from cos2x

  32. IrishBoy123
    • one year ago
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    |dw:1440019749527:dw|

  33. xapproachesinfinity
    • one year ago
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    cos2x=cos^2x-sin^2x

  34. xapproachesinfinity
    • one year ago
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    factor cos^2x to get cos^2x(1-tan^2x)

  35. xapproachesinfinity
    • one year ago
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    that's one step

  36. xapproachesinfinity
    • one year ago
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    recall that cos^2x=1/sec^2x

  37. xapproachesinfinity
    • one year ago
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    but again you sure it is (1+tan^2x)^2? make sure

  38. xapproachesinfinity
    • one year ago
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    should be only 1+tan^2x

  39. anonymous
    • one year ago
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    hh ya realy sure

  40. anonymous
    • one year ago
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    i need to proven the answer is cos2x

  41. xapproachesinfinity
    • one year ago
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    |dw:1440020130101:dw|

  42. anonymous
    • one year ago
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    yup

  43. xapproachesinfinity
    • one year ago
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    i got 1-tan^2x/1+tan^2x=cos^2 not square the bottom

  44. xapproachesinfinity
    • one year ago
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    it cannot be right the way you wrote it please make sure post the picture yo getting u all confused now hhhh

  45. anonymous
    • one year ago
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    but still can get the answer as cos2x jz dono the way how to do

  46. xapproachesinfinity
    • one year ago
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    no it can't if my result is correct that cannot be true

  47. xapproachesinfinity
    • one year ago
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    unless you have a different question

  48. anonymous
    • one year ago
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    the last picture you post is my question

  49. IrishBoy123
    • one year ago
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    screenshot, or url

  50. IrishBoy123
    • one year ago
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    if i had a penny....

  51. xapproachesinfinity
    • one year ago
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    please screenshot that thing man we got confused now

  52. xapproachesinfinity
    • one year ago
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    |dw:1440020383353:dw| if you are talking about this the question is wrong not an identity

  53. anonymous
    • one year ago
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    ya this is my question as exam

  54. freckles
    • one year ago
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    does it say to disprove or to prove?

  55. freckles
    • one year ago
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    or does it just say to show?

  56. xapproachesinfinity
    • one year ago
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    well depends on what the question really states perhaps it want to you see whether that is an identity or not

  57. xapproachesinfinity
    • one year ago
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    so to answer this it is not true not an identity

  58. anonymous
    • one year ago
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    |dw:1440020646681:dw|

  59. anonymous
    • one year ago
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    if like this?

  60. xapproachesinfinity
    • one year ago
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    look if it is not an identity no matter what you try you won't get there haha

  61. anonymous
    • one year ago
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    so sad

  62. IrishBoy123
    • one year ago
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    |dw:1440020700278:dw|

  63. anonymous
    • one year ago
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    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
    • one year ago
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    there should be *every * number in answer, if it was true. yes? x = 0 works. !!

  65. freckles
    • one year ago
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    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
    • one year ago
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    thanks @freckles

  67. freckles
    • one year ago
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    if you meant \[\frac{1-\tan^2(x)}{1+\tan^2(x)}=\cos(2x) \] we would have had more luck

  68. freckles
    • one year ago
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    because this is a true equation

  69. freckles
    • one year ago
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    on the left hand side's domain of course

  70. anonymous
    • one year ago
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    \(\dfrac{1-tan^2(x)}{(1+tan^2(x))^2}\\=\dfrac{1-tan^2(x)}{sec^4(x) }\\= \dfrac{1}{sec^4x}-\dfrac{tan^2x}{sec^4x}\\= cos^4x-cos^2xsin^2x\\=cos^2(x)(cos^2(x)-sin^2(x) )= cos^2(x) (cos(2x))\) No way for you to get cos (2x) only.

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