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If x=sectheta "and " y=cosec theta +cot...

If `x=sectheta "and " y=cosec theta +cottheta`, then prove that `xy+1=y-x`.

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`xy+1=((1-sintheta)/costheta)((1-costheta)/sintheta)+1=(1-sintheta+costheta)/(sinthetacostheta)`
`=((sin^2theta+cos^2theta))/(sinthetacostheta)-((sinthetacostheta))/(sinthetacostheta)`
`=(tantheta+cottheta)-(sectheta-cosectheta)`
`=(cosectheta+cottheta)-(sectheta-tantheta)`
`=y-x`
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