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When proving something....... (C3)

given that cosy=sin(x+y)cos \textrm{y} = sin \textrm{(x+y)}, show that tany=secx−tanxtan \textrm{y} = sec \textrm{x} - tan \textrm{x}

when proving this, am I allowed to assume that tany=secx−tanxtan \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.

sinxcozy=1cosx−sinxcosx\frac{sin \textrm{x} }{coz \textrm{y}} = \frac{1}{cos \textrm{x} } - \frac{sin \textrm{x} }{cos \textrm{x} }

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

sinycosx=cosy−sinxcosy sin \textrm{y} cos \textrm{x} = cos \textrm{y} - sin \textrm{x} cos \textrm{y}

cosxsiny+sinxcosy=cosycos \textrm{x} sin \textrm{y} + sin \textrm{x} cos \textrm{y} = cos \textrm{y}

sin(x+y)=cosysin \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)
(edited 13 years ago)
Reply 1
Avatar for Noble.
Noble.
17
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
(edited 13 years ago)
Reply 2
Avatar for ElMoro
ElMoro
18
Yeah you can do it that way but you couldv'e done it backwards aswell.
Reply 3
Avatar for Libertine
Libertine
8
Just write down your working in reverse and you've proved it forwards.
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:
Libertine
Just write down your working in reverse and you've proved it forwards.

ahha yh that's true :biggrin:
Reply 6
Avatar for Papkin
Papkin
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)
(edited 13 years ago)
Reply 7
Avatar for Noble.
Noble.
17
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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