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Prove that (sintheta+cosectheta)^2+(cost...

Prove that `(sintheta+cosectheta)^2+(costheta+sectheta)^2ge9`.

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`(sintheta+cosectheta)^2+(costheta+sectheta)^2`
`=sin^2theta+cosec^2 theta+2+cos^2theta+sec^2theta+2`
`=(sin^2theta+cos^2theta)+(cosec^2theta+sec^2theta)+4`
`=5+1+tan^2thetta+1+cot^2theta`
`=7+(tantheta-cottheta)^2+2`
`=9+(tantheta-cottheta)^2ge9`
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