cosec theta – cot theta whole square = 1-cos theta/1+cos theta

(Cosec-Cot)^2=1-Cos/1+Cos
L.H.S.= (Cosec-Cot)^2
(1/Sin-Cos/Sin)^2
(1-Cos)^2/(Sin)^2
(1-Cos)^2/Sin^2
(1-Cos)^2/(1-Cos2)
(1-Cos)^2/(1-Cos)(1+Cos)
(1-Cos)/(1+Cos)=R.H.S.
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(Cosec-Cot)^2=1-Cos/1+Cos
L.H.S.= (Cosec-Cot)^2
(1/Sin-Cos/Sin)^2
(1-Cos)^2/(Sin)^2
(1-Cos)^2/Sin^2
(1-Cos)^2/(1-Cos2)
(1-Cos)^2/(1-Cos)(1+Cos)
(1-Cos)/(1+Cos)=R.H.S.
More
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