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Prove that: {1+cottheta-s e c(pi/2+theta...

Prove that: `{1+cottheta-s e c(pi/2+theta)}{1+cottheta+s e c(pi/2+theta)}=2cottheta`

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`L.H.S. = (1+cot theta - sec(pi/2+theta))(1+costheta+sec(pi/2+theta))`
`=(1+cot theta + cosecsectheta)(1+costheta-cosectheta)`...[As `sec(pi/2+theta) = -cosectheta`]
`=(1+cottheta)^2 - (cosectheta)^2`
`=1+cot^2theta+2cot theta - cosec^2theta`
`=cosec^2theta+2cottheta - cosec^2 theta`...[As `1+cot^2theta = cosec^2theta`]
`=2cot theta = R.H.S.`
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