prove that
tan0+sec0-1/tan0-sec0+1=1+sin0/cos0
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LHS=sin0-cos0+1/sin0+cos0-1
on dividing by cos0 up and down,then
tan0+se0-1/tan0-sec0+1
= sec0+tan0-(sec20-tan20)/tan0-sec0+1
= sec0+tan0-{(sec0+tan0)(sec0-tan0)}/tan0-sec0+1
=sec0+tan0(1-sec0+tan0)/tan0-sec0+1
=sec0+tan0*(sec0-tan0)/(sec0-tan0)
=(sec20-tan20)/(sec0-tan0)
=1/sec0-tan0)
=RHS
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