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Trig problems giving a hard time.

  1. Jul 24, 2013 #1
    I was having some free time and decided to do some mathematics from my high school mathematics book.These two problems remained, and I am completely clueless to the solution approach.

    1. The problem statement, all variables and given/known data

    A. If sin(θ)-cos(θ)=1, prove that sin(θ)+cos(θ)=±1
    B. If tan(θ)+sec(θ)=10, prove that sin[itex]^{2}[/itex](θ)+cos[itex]^{2}[/itex](θ)=1

    2. Relevant equations



    3. The attempt at a solution

    The approach to both problems were similar, I squared both sides of the given equations, and used trig identities at an attempt of simplifying.

    That got me nowhere. :frown:

    Pointers would be helpful. :smile:
     
    Last edited: Jul 24, 2013
  2. jcsd
  3. Jul 24, 2013 #2

    haruspex

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    That certainly works for A. If you still can't see it, please post your working.
    For B, pay close attention to what is to be proved.
     
  4. Jul 24, 2013 #3
    Found a way for A:

    sin(θ)-cos(θ)=1
    [Squaring]
    sin[itex]^{2}[/itex](θ)-2sin(θ)cos(θ)+cos[itex]^{2}[/itex](θ)=1=sin[itex]^{2}[/itex](θ)+cos[itex]^{2}[/itex](θ)
    sin[itex]^{2}[/itex](θ)+cos[itex]^{2}[/itex](θ)=sin[itex]^{2}[/itex](θ)+2sin(θ)cos(θ)+cos[itex]^{2}[/itex](θ)
    1=(sin(θ)+cos(θ))[itex]^{2}[/itex]
    [Taking square roots]
    sin(θ)+cos(θ)=[itex]\pm[/itex]1

    For B, the 'to prove' equation is an identity but getting it from the given expression is being a problem
    because as I square the both sides , it gets messier and hopeless.
     
    Last edited: Jul 24, 2013
  5. Jul 24, 2013 #4

    Dick

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    If the equation to be proved is an identity, you don't have to get it from the other expression. It's just plain always true.
     
  6. Jul 24, 2013 #5
    Yes, it is. But I'll look for the solution and post it here as soon as i get it . :smile:

    EDIT:
    the question seems to have been removed from the new edition of the book, mine was an old one.
     
    Last edited: Jul 24, 2013
  7. Jul 24, 2013 #6

    Dick

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    There's really nothing to look for or get. This is exactly like proving "If x=2 then x=x." x=x is true regardless of whether x=2 is true. So "If x=2 then x=x." is a true statement.
     
  8. Jul 24, 2013 #7

    Dick

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    Removing it is a good idea. In the context of proving trig stuff, it's only going to cause confusion.
     
  9. Jul 24, 2013 #8
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