prove that cotA + cosecA -1/ cotA - CosecA + 1 = 1 + cosA - sinA

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

= (cos²A - sin²A + sinAcosA)/sinAcosA

= (cosA(1 + sinA))/sinAcosA

sorry hv to go solve it completely later hope this musch will help u a bit

i didnt understand the second and third step...can u plz explain it...

Alternative method:

cot A + cosec A - 1 /  cot A - cosec A + 1   =  1 + cos A / sin A  

how did cosA-SinA came 3 times after rationalising??

shriyansh1994 thats during the time of rationalising ,The time of multiplication it seems its 3 times ,we are simplifying it shriyansh1994 observe carefully.One student had asked the same doubt what you asked but I gave the same solution.He was very satisfied with my same solution which I gave to you and he gave me a thumb up .After observing if you are satisfied do give a thumb up and if any more confusion just mention .

Gud imad.... thumbs up fr u....

Imad your answer is wrong check what you have proved and what you needed to proove.

NITIN the answer I have given is absolutely correct .But in the question given by shriyansh1994 the RHS is not 1 + cosA - sinA but it must be 1 + cos A / sin A .Do observe my solution carefully and do give you suggestion then,IF YOU ARE SATISFIED DO GIVE A THUMB UP.

yes he is right.....i verified the queston it is 1+cosA/sinA

Imad,after rationalising u got

{(cosA- sinA)(cosA+sinA) +(cosA- sinA) +(cosA- sinA) +1} /[(cosA+sinA) – 1][(cosA+sinA) +1]

but how you got  the numerator {(cosA- sinA)(cosA+sinA) +(cosA- sinA) +(cosA- sinA) +1}                                                   is it like this know?? {(cosA- sinA)(cosA+sinA) +(cosA- sinA) +(cosA+ sinA) +1}   ?????