Please follow the given link :

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Alternative method:

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

**cot A + cosec A - 1 / cot A - cosec A +**1

**( Rationalising it by"(cosA+sinA) +1")**

^{2}A- sin

^{2}A)+2cosA+

^{2}-1

^{2}A-(1- cos

^{2}A) + 2cosA+1} / (cos

^{2}A+sin

^{2}A+2sinA cosA) -1

^{2}A-

^{2}A + 2cosA+

^{2}A + 2cosA / 2sinA cosA

**1 + cos A / sin A**

**LHS = RHS**

**(Hence proved)**- 60

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 .

- -2

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} ?????

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LHS = (cotA + cosecA - 1)/(cotA - cosec A + 1)

**[**cotA + cosecA + (cot^{2}A - cosec^{2}A)**] / ****(cotA – cosecA + 1) **** **** ****{because cot ^{2}A – cosec^{2}A = -1}**

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

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

(cotA + cosecA)

cosA / sinA + 1 / sinA

1 + cosA / sinA

- 45