cosA - sinA + 1 / cosA + sinA - 1 = cosecA + cotA
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Answer:
use identity 1+cot^2A=cosec^2A
LHS= (cotA-1+cosecA)/(cotA+1-cosecA)
(by dividing numerator and denominator by sinA)
=(cotA+cosecA-1)/(cotA+1-cosecA)
=(cotA+cosecA-(cosec^2A-cot^A))/(cotA+1-cosecA)
=(cotA+cosecA)(cotA+1-cosecA)/(cotA+1-cosecA)
=cotA+cosecA
=RHS
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