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Identities- Ugh! 1÷cscθ−cotθ=1+cosθ÷sinθ

  • one year ago
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  1. Tushara
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    r u missing any brackets?

    • one year ago
  2. ZeHanz
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    It should be:\[\frac{ 1 }{ \csc \theta - \cot \theta }=\frac{ 1+\cos \theta }{ \sin \theta }\]Let's begin at the left hand side:\[\frac{ 1 }{ \csc \theta - \cot \theta }=\frac{ 1 }{ \frac{ 1 }{ \sin \theta }-\frac{ \cos \theta }{ \sin \theta } }=\frac{ 1 }{ \frac{ 1-\cos \theta }{ \sin \theta } }=\frac{ \sin \theta }{ 1- \cos \theta }\]This looks much better, although it is not quite the right hand side yet... Hint: multiply numerator and denominator of the last fraction with (1+cosθ)/(1+cosθ):\[\frac{ \sin θ }{ 1-\cos θ } \cdot \frac{ 1+\cos θ }{ 1+\cos θ }= ...\]After just a few small steps, you'll have got to the right hand side of the identity!

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