Question

lim {cosec(x) - cot(x)}
x-1 ​

Answer 1

first of all please correct your question ;

lim {cosec(x) - cot(x)}

x->0

now ;

1/sinx - cosx/sinx

(1-cosx)/sinx

when we put x=0

then we get 0/0 form .

so as we know for 0/0 form use D-L hospital rule :

d/dx ( 1-cosx) / d/dx(sinx)

= ( 0+sinx ) / cosx

= Sin (0) / cos (0)

= 0/1

= 0