anonymous
  • anonymous
Prove - tan^2(x) + sec^2(x) = 1 by working on one side to match the other using identities.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[- \tan^2x + \sec^2x = 1\]
anonymous
  • anonymous
\[- \tan^2x + \sec^2x = 1\]
Nnesha
  • Nnesha
sec^2 theta = what ? remember the identity ?

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anonymous
  • anonymous
1/cos^2x
Nnesha
  • Nnesha
well that's reciprocal of sec but it's okay we can use that too!! tan^2 =what ?
anonymous
  • anonymous
sin^2x/cos^2x
anonymous
  • anonymous
or 1/cot^2x
Nnesha
  • Nnesha
yes right so replace tan and sec with that \[\huge\rm -\frac{ \sin^2x }{ \cos^2x } +\frac{ 1 }{ \cos^2x}\] find the common denominator
anonymous
  • anonymous
cos^2x?
Nnesha
  • Nnesha
ohh well not gonna work should use the identity i guess
Jhannybean
  • Jhannybean
You could also use the fact that \(\sf sec^2(\theta) = tan^2(\theta) +1\) and then substitute this in place of \(\sf \sec^2(\theta)\)
anonymous
  • anonymous
thats true, thanks
Jhannybean
  • Jhannybean
\[\sf -tan^2(\theta)+\sec^2(\theta) = 1\]\[\sf -\tan^2(\theta) +\color{red}{\tan^2(\theta) +1}=1\]
anonymous
  • anonymous
Wow... The one identity I didn't think of solved it so easily. Thank you!
Nnesha
  • Nnesha
\[\huge\rm \frac{ -\sin^2x +1}{ \cos^2 }\] use the special identity sin^2x+cos^2x =1 solve for cos^2
Jhannybean
  • Jhannybean
No problem :)
Nnesha
  • Nnesha
here you can copy these identities http://www.math.com/tables/trig/identities.htm you weren't familiar with this so that's why i thought better to write interms of sin and cos
Jhannybean
  • Jhannybean
That's a good way to approach it too. @Nnesha :)
anonymous
  • anonymous
Thanks that will help too @Nnesha
Nnesha
  • Nnesha
yw :=)

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