prove that ÷ cosec a+cot a+1/cosec a-cot a+1=1+cos a/sin a
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L.H.S. =cosA−sinA+1cosA+sinA−1
=cotA−1+cosecAcotA+1−cosecA " " (divide each term of Nr. And Dr . By sin A)
(cotA cosecA)−1(cotA−cosecA)+1
=(cotA+cosecA)−(cosec2A−cot2A)(cotA−cosecA+1)(∵cosec2A−cot2A=1)
=(cosecA+cotA)(1−cosecA+cotA)(cotA−cosecA+1)
=(cosecA+cotA)(1−cosecA+cotA)(cotA−cosecA+1)
=cosecA+cotA=R.H.S.
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