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kjuchiha

  • 2 years ago

Use basic identities to simplify the expression. (cos^2(theta))/(sin^2(theta))+ csc(theta) sin(theta)

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  1. kjuchiha
    • 2 years ago
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    \[\frac{ \cos^2(\theta) }{ \sin^2(\theta)}+\csc(\theta) \sin(\theta)\]

  2. Loser66
    • 2 years ago
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    csc = 1/sin, replace it, first, then I guide you more

  3. zzr0ck3r
    • 2 years ago
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    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)

  4. doulikepiecauseidont
    • 2 years ago
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    \[\frac{ \cos^2 (\theta)}{ \sin^2(\theta) }+\csc (\theta)\sin(\theta)\]

  5. doulikepiecauseidont
    • 2 years ago
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    \[\csc(\theta)=\frac{ 1 }{ \sin(\theta)}\]

  6. doulikepiecauseidont
    • 2 years ago
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    skipping the fraction for a second \[\frac{ 1 }{ \sin(\theta) }*\sin(\theta)=1\]

  7. doulikepiecauseidont
    • 2 years ago
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    and now \[\frac{ \sin^2(\theta) }{ \cos^2(\theta) }=\tan^2(\theta)\]

  8. doulikepiecauseidont
    • 2 years ago
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    \[ \tan^2(\theta)+1=\csc^2(\theta) \]

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