cosA-sinA+1÷cosA+sinA-1=cosecA+cotA
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Step-by-step explanation:
LHS = cosA-sinA+1/cosA+sinA-1
divide both numerator and the denominator by sinA.
=cotA-1+cosecA/cotA+1-cosecA
={cotA+cosecA-(cosec²A-cot²A)} / (cotA-cosecA+1)
={(cotA+cosecA)-(cosecA+cotA)(cosecA-cot)} / (cotA-cosecA+1)
=[(cotA+cosecA){1-(cosecA-cotA)}] / (cotA-cosecA+1)
=(cotA+cosecA)(1-cosecA+cotA) / (cotA-cosecA+1)
=cotA+cosecA
RHS
LHS=RHS
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