anonymous
  • anonymous
Verify The Identity Cos(x)+Sin(x)Tan(x)=Sec(x) Can someone please help explain to me how to verify an identity?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
try drawing a triangle and label the ratios and go from there....
anonymous
  • anonymous
Ok.. I guess I'm confused by what ratios? No numbers were given. I know you probably would start with the left side of this equation (maybe divide each side by tan(x)?)
anonymous
  • anonymous
use this, and create your ratios...Example Sin=b/c http://3.bp.blogspot.com/_kjNvt_oqTsE/TORcXMO_H6I/AAAAAAAAACo/CbLIh4wjhaI/s1600/Image289.gif

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anonymous
  • anonymous
put it in those terms and it should be easier for you to prove...
anonymous
  • anonymous
Proving a proof cannot be done using what is given, it must be changed to new terms...Just like the definition of a word can't include the word....
anonymous
  • anonymous
does it matter where I put each term?
anonymous
  • anonymous
put them in the order of the identity...So, Cosx becomes (a/c) etc...
anonymous
  • anonymous
oh ok...
anonymous
  • anonymous
so I have cosx=a/c sinx=b/c and tanx= c/?
anonymous
  • anonymous
the tangent is what? Its the opposite side/adjacent side... (b/a)
anonymous
  • anonymous
So...(a/c)+(b/c)(b/a) and solve...
anonymous
  • anonymous
OHHH ok! and I want it to equal secx which is equal to what? a/b?
anonymous
  • anonymous
OHHH ok! and I want it to equal secx which is equal to what? a/b?
anonymous
  • anonymous
i have confused you, and I'm sorry...You need to see that Tangent equals (sin/cos) and make that substitution.
anonymous
  • anonymous
Once you see that, then the fractions become easier to work, because they are impossible to work without that substitution.
anonymous
  • anonymous
ok so i understand that now...
anonymous
  • anonymous
Completely ignore the answer Secant side of the equation, and solve the fractional problem...and you'll determine what secant is in terms of fractions, which is what they want....
anonymous
  • anonymous
So, basically, this... sin x tan x + cos x = sin x (sin x / cos x) + cos x = ( sin^2(x) / cos x ) + cos x = [ sin^2(x) + cos^2(x) ] / cos x = 1 / cos x = sec x
anonymous
  • anonymous
Alright so I was close on my paper... I think I just mixed up the terms. Therefore this is an identity. Thank you!
anonymous
  • anonymous
Ok one more Question...does theta basically resemble the x in the previous problem?

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