Question

prove that cosa+sina-1/cosa- sina+1=coseca+cota

Answer 1

by this method u can get the answer...

Answer 2

hope it helped u
(cosA - sin A + 1)/(cosA + sinA - 1)
Divide numerator and denominator by sinA, we get
=(cosA/sinA - sinA/sinA + 1/sinA)/ (cosA/sinA + sinA/sinA - 1/sinA)
=(cotA - 1 + cosecA)/(cotA+1- cosecA)
= ​(cotA + cosecA- 1)/cotA + 1 - cosecA)​
We know that cosec2A - cot2A= 1
so we replace 1 by cosec2A - cot2A, we get
=[cotA + cosecA - (cosec2A - cot2A)]/(cotA - cosecA + 1)
=[(cotA + cosecA)- (cosecA - cotA)(cosecA+cotA)]/(cotA -cosecA + 1)
taking cosecA + cotA common, we get
=cosecA + cotA[1-(cosecA - cotA)]/(cotA - cosecA + 1)
=cosecA + cotA(1-cosecA + cotA)/(cotA - cosecA +1)
=cosecA + cotA  Proved         {1-cosecA + cotA cancelled out}