Question

prove that cot²A/(cosec+1)²=1 - sinA /1+sin A​

Answer 1

hope this ans will be helpful ...

Answer 2

$\frac{cot^2A}{(cosec+1)^2}=\frac{1-sinA}{1+sinA}\\ \\LHS:$

$=\frac{cot^2A}{(cosecA+1)^2}\\\\=\frac{cosec^2A-1}{(cosecA+1)^2}\\\\=\frac{cosec^2A-1}{(cosecA+1)(cosecA+1)}\\ \\=\frac{(cosecA-1)(cosecA+1)}{(cosecA+1)(cosecA+1)}\\\\=\frac{(cosecA-1)}{(cosecA+1)}\\ \\=\frac{1/sinA-1}{1/sinA+1}\\ \\=\frac{(1-sinA)/sinA}{(1+sinA)/sinA}$

sinA gets cancelled :

$=\frac{1-sinA}{1+sinA}$

LHS = RHS .

Hence , proved .