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Trig Identities

  • Thread starter ihatemath
  • Start date
  • #1
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ok ... heres my problem
i need to prove that the LHS = RHS


sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

i tried to use the pythagarean identies and substitute the 1 and 2
but tht isnt getting me anywhere .. plz help
 

Answers and Replies

  • #2
Cyosis
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If you don't list the arguments of the functions we can't help you, also show the steps you've taken so far.
 
  • #3
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ummm ok .. here's what i got


sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

LHS :

= sin^2 + cos + cos - sin^2 - cos^2 / 1 + sin^2 + cos^2 + cos - cos^2
... here i cancelled the "sin^2" and " - sin^2" on the top and in the bottom i cancelled the "cos^2" and " - cos^2"

= cos + cos - (cos)(cos) / 1 + sin^2 + cos

= cos + cos - cos^2 / sin^2 + cos^2 + sin^2 + cos

= cos + cos / sin^2 + sin^2 + cos

...... I dont noe what to do from here ... am i even tackling this problem the right way ??

RHS :

1 / 1 + sec

= 1 / 1 + 1/cos
= 1 + cos .... no problems here .. jus the LHS
 
  • #4
Cyosis
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You forgot the arguments. Sin does not exist, sin(x) does etc.
 
  • #5
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there all sin(x) or cos(x) :tongue2:
 
  • #6
Cyosis
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Okay then we're arriving at the next problem. I have a feeling that some brackets are missing, for example what is 1/1+sec(x) is it [tex]1+\sec(x)[/tex] or [tex]\frac{1}{1+\sec x}[/tex]. Same goes for the right hand side. Use brackets to make divisions clear.
 
  • #7
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itz

[tex]\frac{1}{1+\sec x}[/tex]
 
  • #8
Cyosis
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Yes, but what about the other side, similar ambiguities exist there. For me to assist you on this problem you will need to take all those ambiguities away.
 
  • #9
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ok ... heres my problem
i need to prove that the LHS = RHS


sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

i tried to use the pythagarean identies and substitute the 1 and 2
but tht isnt getting me anywhere .. plz help
Are you trying to prove that
[tex]sin^2(x) + 2cos(x) - \frac{1}{2} + cos(x) - cos^2(x) = \frac{1}{1 + sec(x)}?[/tex]

That's actually the most reasonable way to interpret what you have written. (You've already told us what you meant on the right-hand side.
 

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