Question

limx-0 1÷x (cot 2x - cosec 2x)

Answer 1

hello friend...

here is the solution,

we have to find
lim x→0 1÷x (cot 2x - cosec 2x) = ?

formula used:-
lim x→0 (tan x)/x = 1
{1- (cos 2x)}= 2sin²x
sin 2x = 2sinx cosx

now here

lim x→0 1÷x (cot 2x - cosec 2x) =
let first solve
( cot 2x - cosec 2x)=
{(cos 2x)/(sin 2x) - 1 /( sin 2x)}
= { (cos 2x -1) / sin 2x}
= {-(1-cos 2x)/ sin 2x}
= { -2 sin²x/2sinxcosx}
= {- (sinx)/(cos x)}
= -tan x

now
lim x→0 1÷x (cot 2x - cosec 2x) =
Lim x→0 1/x (-tan x)
= Lim x→0 (-tan x)/x
= - Lim x→0 (tan x)/x
= -1

hence.
lim x→0 1÷x (cot 2x - cosec 2x) = -1

## Hope it helps##