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    given that cos \textrm{y} = sin \textrm{(x+y)}, show that tan \textrm{y} = sec \textrm{x} - tan \textrm{x}

    when proving this, am I allowed to assume that tan \textrm{y} = sec \textrm{x} - tan \textrm{x} is true??

    like... prove it backwards? I don't really know how to prove this kind of stuff :confused: help

    i.e.

    \frac{sin \textrm{x} }{coz \textrm{y}} = \frac{1}{cos \textrm{x} } - \frac{sin \textrm{x} }{cos \textrm{x} }

     = \frac{1 - sin \textrm{x} }{cos \textrm{x} }

     sin \textrm{y} cos \textrm{x} = cos \textrm{y} - sin \textrm{x} cos \textrm{y}

    cos \textrm{x} sin \textrm{y} + sin \textrm{x} cos \textrm{y} = cos \textrm{y}

    sin \textrm{(x+y)} = cos \textrm{y}

    is this proved then? or did i do it the wrong way?


    (edit: i don't know why I posted this in Maths Exams section... someone please move this to Maths forum! thanks)
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    Yes, you can do that, although it's better to try doing it the way it's presented.

    You know the expansion for sin(A+B) = sinAcosB + cosAsinB
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    Yeah you can do it that way but you couldv'e done it backwards aswell.
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    Just write down your working in reverse and you've proved it forwards.
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    (Original post by Noble.)
    Yes, you can do that, although it's better to try doing it the way it's presented.

    You know the expansion for sin(A+B) = sinAcosB + cosAsinB
    yep but somehow doing it backwards makes it easier for me lol don't know why :p:
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    (Original post by Libertine)
    Just write down your working in reverse and you've proved it forwards.
    ahha yh that's true
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    If you do so, you should point out in your proof that all tranformations are equivalent. Otherwise the proof will be incorrect.(You show only one side of equivalence-implication)
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    (Original post by IAmTheChosenOne)
    yep but somehow doing it backwards makes it easier for me lol don't know why :p:
    When proving it forwards, you still need to be 'a few steps ahead', you can't just plug in any old identity and hope it works. So I think you'll find most people look at both ends of the proof. When proving that, I'd write the end-point in terms of cosine/sine, do the same with the given equation, and see how I could get there.
 
 
 
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