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Prove that: (sin theta-cosec theta)^2+(c...

Prove that: `(sin theta-cosec theta)^2+(cos theta-sec theta)^2=cot^2 theta+tan^2 theta-1`

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`L.H.S. =(sintheta-cosectheta)^2+(costheta-sectheta)^2`
`=(sintheta-1/sintheta)^2+(costheta-1/costheta)^2`
`=sin^2theta+1/sin^2theta-2+cos^2theta+1/cos^2theta-2`
As `sin^2theta+cos^2theta =1 `,
So, our expression becomes,
`=1-2-2+1/sin^2theta+1/cos^2theta`
`=cosec^2theta+sec^2theta-3`
As, `cosec^2theta = 1+cot^2theta, sec^2theta = 1+ tan^2theta`, so, our expression becomes,
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