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

Explanation

`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.`