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Prove that : 1+(cot^(2)alpha)/(1+"cosec...

Prove that : `1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha`

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L.H.S. `=1+(cot^(2)alpha)/(1+"cosec"alpha)=1+("cosec"^(2)alpha-1)/(1+"cosec"alpha-1)`
`=1+(("cosec"alpha-1)("cosec"alpha+1))/(1+"cosec"alpha)=1+("cosec"alpha-1)`
`="cosec"alpha=R.H.S.`
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