prove that - cos + cosec -1 /cot -cosec +1 =1+cos/sin
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L.H.S.
= cos+cosec-1/cot-cosec+1
= cos+1/sin-sin/cos-1/sin+1.
{cosec=1/sin, 1/ cot=tan=sin/cos, & sin^2+cos^2=1}
= (sin cos^2 + cos - sin^2 - cos + sin^2 + cos^2)/sin cos
= {cos(sin+cos)}/sin cos
= 1+cos/sin
= R.H.S.
Hence , R.H.S.=L.H.S.
Hence proved!
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