Prove that `(cos e ctheta-sintheta)(sectheta-costheta)=1/(tantheta+cottheta)dot`

Explanation

`L.H.S = ( cosec theta – sin theta )( sec theta – cos theta)`

` = ( 1/(sin theta) - sin theta) (1/(cos theta) – cos theta)`

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

` = (cos^2 theta sin^2 theta)/(sin theta cos theta)`

`= cos theta sin theta`

`R.H.S= 1/(tan theta + cot theta)`

` = 1/ ((sin theta / cos theta) + (cos theta / sin theta))`

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

...