Question

answer the question briefly

Answer 1

(cosA-sinA+1)/(cosA+sinA-1) = cosecA+cotA

L. H. S =

Diving by sinA in numerator, we get

(cotA-1+cosecA)/(cotA+1-cosecA)

cotA+cosecA-1 / (cotA-cosecA+1)

cotA+cosecA-(cosec²A-cot²A)/(cotA-cosecA+1)

cotA+cosecA-[(cosecA+cotA)(cosecA-cotA)] / (cotA-cosecA+1)

Taking common cosecA+cotA in numerator, we get

cosecA+cotA [(1-cosecA +cotA)] /(cotA-cosecA+1)

cosecA+cotA [(1-cosecA+cotA)] /(1-cosecA+cotA)

Hence, (1-cosecA+cotA) will be canceled in numerator and denomination and Answer will be cosecA +cotA.

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