anonymous
  • anonymous
Use basic identities to simplify the expression. (cos^2(theta))/(sin^2(theta))+ csc(theta) sin(theta)
Precalculus
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\frac{ \cos^2(\theta) }{ \sin^2(\theta)}+\csc(\theta) \sin(\theta)\]
Loser66
  • Loser66
csc = 1/sin, replace it, first, then I guide you more
zzr0ck3r
  • zzr0ck3r
csc(x)*sin(x)=(1/sin(x))sin(x) = 1 cos^2(x)/sin^2(x) = cot^2(x) so cot^2(x) + 1 now how can we get that out of cos^2(x)+sin^2(x)=1 divide everything by sin^2(x) cot^2(x)+1 = (1/sin^2(x)) = csc^2(x)

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anonymous
  • anonymous
\[\frac{ \cos^2 (\theta)}{ \sin^2(\theta) }+\csc (\theta)\sin(\theta)\]
anonymous
  • anonymous
\[\csc(\theta)=\frac{ 1 }{ \sin(\theta)}\]
anonymous
  • anonymous
skipping the fraction for a second \[\frac{ 1 }{ \sin(\theta) }*\sin(\theta)=1\]
anonymous
  • anonymous
and now \[\frac{ \sin^2(\theta) }{ \cos^2(\theta) }=\tan^2(\theta)\]
anonymous
  • anonymous
\[ \tan^2(\theta)+1=\csc^2(\theta) \]

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