anonymous
  • anonymous
Which identity is not used in the proof of the identity? 1 + cot^2 theta = csc^2 theta
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
here is the proof: http://puu.sh/3cMf2.png
campbell_st
  • campbell_st
a simple proof is to start with \[\sin^2(x)+ \cos^2(x) = 1\] divide each term by sin^2(x) gives \[1 + \frac{\cos^2(x)}{\sin^2(x)} = \frac{1}{\sin^2(x)}\] which gives \[1 + \cot^2(x) = \csc^2(x)\] so 1 ratio not used is tan^2(x) and perhaps sec^2(x)
anonymous
  • anonymous
i need to know which identity is not used to find the proof. for example, cotangent identity, Pythagorean identity, etc

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campbell_st
  • campbell_st
well the proof doesn't use sec(x) or tan(x) and it seems a complicated proof...
anonymous
  • anonymous
my options are cotangent identity Pythagorean identity reciprocal identity and tangent identity
anonymous
  • anonymous
TAngent Identity. It means the usage of tan
anonymous
  • anonymous
Cotangent means the using of various properties of cot: cot^2x+1=cosec^2x Pythagoran is sin^2x+cos^2x=1 Reciprocal is 1/sin^2x=csc^2x So only tangent is left. :)
anonymous
  • anonymous
I love medals! xD
anonymous
  • anonymous
can you help me with one more?
anonymous
  • anonymous
http://puu.sh/3cNKR.png
anonymous
  • anonymous
@kutabs
anonymous
  • anonymous
Option 3 is the only correct one the rest are wrong. Eg: sin^2x=cos^2x-1 which gives, cos^2x-sin^2=1 (Not possible as sin^2x+cos^2x=1 Phthagoran identity). Similarly you could prove the others wrong.
anonymous
  • anonymous
Thank you so much!

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