prove that-
cosA-sinA+1÷cosA+sinA-1
=cosecA+cotA
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LHS,
cosA-sinA +1
=> ---------------------
cosA+sinA-1
cosA/sinA - sinA/sinA +1/sinA
=> ---------------------------------------------
cosA/sinA +sinA/sinA - 1/sinA
cotA - 1 + cosecA
=> -----------------------------
cotA + 1 -cosecA
(cosecA+cotA) - (cosec²A - cot²A)
=> ---------------------------------------------
cotA+1-cosecA
(cosecA+cotA)-(cosecA+cot)
(cosecA-cotA)
=> ------------------------------------------
1-cosecA+cotA
(cosecA+cotA)(1-cosecA+cotA)
=> --------------------------------------------
(1-cosecA+cotA)
=> cosecA+cotA
=> RHS,
PROVED
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