Answer 1

L.H.S =(1 + cot θ – cosec θ)(1+ tan θ + sec θ)

= `(1 + costheta/sintheta - 1/sin theta)(1+sin theta/cos theta + 1/cos theta)`

`= ((sintheta + costheta - 1)/sintheta)((costheta + sintheta +1)/costheta)`

`= 1/(sinthetacostheta) ((sinthetacostheta+sin^2theta + sin theta+cos^2theta),(+sinthetacostheta+costheta-costheta - sin theta -1))`

`= 1/(sinthetacostheta) (2sinthetacostheta + (sin^2theta + cos^2 theta) - 1)`

`= 1/(sin thetacostheta) (2sinthetacostheta + 1 - 1)`

`= (2sin thetacostheta)/(sin thetacos theta)`

= 2

= R.H.S