Evaluate
x → 0 lim csc x tan x
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
yes exactly
We can solve it in this way :- l i m x → 0 c o s e c x . t a n x = l i m x → 0 c o s e c x . c o s x s i n x l i m x → 0 s i n x 1 c o s x s i n x Cancelling sin x we get l i m x → 0 c o s x 1 l i m x → 0 s e c x now putting x = 0 we get, x = 1
as x->0 sinx->x and tanx->x therefore csc x.tan x=tan x/sin x=x/x=1
cscxtanx=secx x=0; sec(0)= 1
cosecx X tanx =1/ cosx ( cos0=1 ) so ans=1
since csc x tan x = 1/cos x and cos x = 1 as x approaches 0, so we'll get 1/1 =1
we may write cosec x inthe term of sin then expand sin and tan using x=0 as the pole using maclurins or tailorsexpansion and put x=0 to get ans 1 eaisly
Problem Loading...
Note Loading...
Set Loading...
Well, you could use l'hopital's... Since csc (0) approaches ∞ and tan (0) approaches 0,
But it's much simplier to use the identity csc x tan x= sec x. And sec(0)=1.