Question

prove that cos theta minus sin theta + 1 / sin theta + cos theta - 1 = 1 divided by cosec theta minus cot theta​

Answer 1

Step-by-step explanation:

cosA-sinA+1/cosA+sinA-1

devide cosA in both numerator & denominator

cotA-1+cosecA/cotA+1-cosecA

={(cotA+cosecA)-1}×(cotA-cosecA)/ {(cotA-cosecA)+1}×(cotA-cosecA)

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

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

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

=-1/-(cosecA-cotA)

=1/cosecA-cotA