1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trig identity questions

  1. Jun 10, 2013 #1
    Hey guys,I need some help on the following trig identities:

    1) sin2x = 2tanx/1+tan^2x

    2) sin2x/sinx - cos2x/cosx = secx

    My attempts:

    1) LS: sin2x



    Not sure if this is right or not. I kind of understand my third step but it just doesn't seem right, any validations? If not, help please.

    2) LS: sin2x/sinx - cos2x/cosx

    2sinxcosx/sinx - ???

    sinx/cosx - ?? i have no idea where to go from here
  2. jcsd
  3. Jun 10, 2013 #2


    User Avatar
    Homework Helper

    Do #1 in reverse, it should be easier, and take little steps, don't make your steps too large. Each step should be small enough to be obvious to the reader.
  4. Jun 10, 2013 #3


    User Avatar
    Science Advisor

    Yes, sin(2x)= 2sin(x)cos(x)

    What? 2 sin(x)/cos(x)= 2 tan(x). Have you changed to the right side now??

    Where did this come from? It is what you want to arrive at but what are you doing to get it?

    Frankly, I don't understand what you are trying to do. Please state exactly what you are doing to go from one step to another.
  5. Jun 10, 2013 #4
    I just stated that I was trying to turn the left side into the right, sorry for the confusion. When I do these I just pick a side then use identities until it is equal to the opposite side.
  6. Jun 10, 2013 #5


    User Avatar
    Science Advisor
    Homework Helper

    hi tg22542! :smile:

    (try using the X2 button just above the Reply box :wink:)
    as verty :smile: says, it would be a lot easier to go from right to left!

    if you must go from left to right, use cos = 1/sec :wink:
    first step is obviously to put them over a common denominator
  7. Jun 10, 2013 #6
    okay so I believe I completed 1)







    good? :)

    thank you guys very much for your help so far, very appreciated
  8. Jun 10, 2013 #7
    nevermind.. just realized the identity I used for sec is actually sec^2..

  9. Jun 10, 2013 #8


    User Avatar
    Education Advisor

    Looks good to me.

    For your other question, do you know any trig identities dealing with cos[2x]? Such as Cos[2x] = Cos[x]^2 - Sin[x]^2 ?
  10. Jun 10, 2013 #9


    Staff: Mentor

    The expressions below are all equal, so you should denote them as such by using =.

    Also, what you wrote below needs parentheses around the terms in the denominator. What you wrote is really this:
    $$\frac{2tan(x)}{1} + sec^2(x)$$
  11. Jun 11, 2013 #10


    User Avatar
    Science Advisor
    Homework Helper

    yes :smile:
    where did this come from? :confused:

    use 1/sec = cos (as i said before)​
  12. Jun 11, 2013 #11
    So could it go :

    RS: 2tanx/1+tan^2x

    =sin^2x/cos^2x + 1/cos^2x ??
  13. Jun 11, 2013 #12


    User Avatar
    Science Advisor
    Homework Helper

    (try using the X2 button just above the Reply box :wink:)
    i honestly have no idea how you got that :confused:

    tg22542, in the exam, you must do one step at a time …

    then the examiner can see what you're doing, and why, and at least give you some marks for getting something right!

    try again, slowwwwly :smile:
  14. Jun 11, 2013 #13
    RS: 2tanx/1+tan^2x

    So I first used the identity tan^2x + 1 = sec^2x


    = 2tanx + sec^2x

    Next I used tanx=sinx/cosx


    2sinx/2cosx + sec^2x

    Now I'm lost, It must equal 2sinx so I clearly have to get the cos to cancel out somehow, but I don't know which identities to use
  15. Jun 11, 2013 #14


    User Avatar
    Science Advisor
    Homework Helper

    correct :smile:

    (except it would be clearer if you used brackets: 2tanx/(1+tan^2x) …

    i suspect that's partly the reason why your next step was wrong …

    as Mark44 has already said, always use brackets (parentheses))


    = 2tanx/sec2x …

    carry on from there :wink:
  16. Jun 11, 2013 #15
    Any idea on which identity to use from these point on? I'm lost :(
  17. Jun 11, 2013 #16


    User Avatar
    Gold Member

    What is tanx equal to? What is sec2x equal to? Now sub in.
  18. Jun 11, 2013 #17
    =(2sinx/2cosx)/(1/cos^2x) ?
  19. Jun 11, 2013 #18


    User Avatar
    Science Advisor
    Homework Helper

    yes :smile:

    (except for one silly mistake :wink:)

    and then?​
  20. Jun 11, 2013 #19
    I have no idea, I feel likei cou,d multiply the top by 2cos leaving me 2sinx2cosx/cos which wou,d give me the answer? Correct?
  21. Jun 11, 2013 #20


    User Avatar
    Science Advisor
    Homework Helper

    tg22542, i don't understand your defeatism

    you say "i have no idea", even though you obviously do have an idea (and it's the correct one) :confused:

    yes, your 1/(1/something) can obviously be cancelled out

    it's your "2"s that need a second look :redface:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Trig identity questions
  1. Trig identity question (Replies: 11)

  2. Trig Identity Question (Replies: 3)