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Proving Trig Identities

  1. Oct 22, 2006 #1
    hey guyz...ok iv been trying to figure this question out for so long...and i jus can't.i get up to a certain point and then i jus get confused.so if anyone can help me that would be great!

    Prov that:
    Cos^2x + Cotx ÷ Cos^2x – Cotx = Cos^2x (tanx) + 1 ÷ Cos^2x (tanx) -1
     
  2. jcsd
  3. Oct 22, 2006 #2
    [tex] \frac{\cos^{2}x + \cot x}{\cos^{2}x-\cot x} = \frac{\cos^{2}x(\tan x)+1}{\cos^{2} x(\tan x) -1} [/tex]

    Convert the left side to sines and cosines:

    [tex] \frac{\cos^{2}x + \frac{\cos x}{\sin x}}{\cos^{2}x - \frac{\cos x}{\sin x}} = \frac{\cos^{2}x\sin x + \cos x}{\sin x}\frac{\sin x}{\cos^{2}x\sin x - \cos x} = \frac{\cos^{2}x\sin x + \cos x}{\cos^{2}x\sin x - \cos x} = \frac{\cos^{2}x(\sin x + \frac{1}{\cos x})}{\cos^{2}x(\sin x - \frac{1}{\cos x})} [/tex].

    Can you go from there?
     
    Last edited: Oct 22, 2006
  4. Oct 22, 2006 #3
    umm ok the first setp i got...but the 2nd one im a little bit confused as to what you did...
     
  5. Oct 23, 2006 #4

    Hootenanny

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    Note that;

    [tex]\cot\theta=\frac{1}{\tan\theta}=\frac{1}{\frac{\sin\theta}{\cos\theta}}=\frac{\cos\theta}{\sin\theta}[/tex]
     
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