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Prove that : (sinalpha+cosalpha)(tanal...

Prove that : `(sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosecα"`.

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L.H.S. `=(sinalpha+cosalpha)(tanalpha+cotalpha)`
`=(sinalpha+cosalpha)((sinalpha)/(cosalpha)+(cosalpha)/(sinalpha))=(sinalpha+cosalpha)((sin^(2)alpha+cos^(2)alpha)/(sinalphacosalpha))`
`=(sinalpha+cosalpha)((1)/(sinalphacosalpha))=(sinalpha)/(sinalphacosalpha)+(cosalpha)/(sinalphacosalpha)`
`=(1)/(cosalpha)+(1)/(sinalpha)=secalpha+"cosec"alpha=R.H.S.`
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