prove cos A-sinA+1÷cosA+sinA-1=cosecA+cotA
sakshi36637:
first multiply and divide by sinA
then multiply nd divide by cotA - cosecA
numerator ko solve kro denominator ko aese hi likh do
then - 1 common lena identity use krk
then rationalise
u will get ur ans
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✔️✔️Here is your ans mate ✔️✔️
cos A- sin A + 1)/(cos A + sin A - 1). Divide both numerator and the denominator by sinA.the sum becomes
(cot A - 1 + cosec A)/(cot A + 1 -cosec A)
=(cosec A + cot A - 1)/(cotA - cosec A +1)
={cosecA+cotA-(cosec^2 A- cot^2 A)}/Dr where Dr=cotA-cosecA+1
={(cosecA+cotA)-(cosecA+cotA)(cosecA-cotA)}/ Dr.
=[(cosecA+cotA){1-(cosecA-cotA)}]/Dr
={(cosecA+cotA)(1-cosecA+cotA)}/Dr
=(cosecA+cotA)(cotA-cosecA+1)/Dr
=(cosecA+cotA).Dr/Dr
=cosecA+cotA
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