Evaluate lim(x tends to zero) cosecx-cotx/x?

1 Answer
maganbhai P.
Mar 10, 2018

#1/2#

Explanation:

Here, #cosecx-cotx=((cosecx-cotx)(cosecx+cotx))/(cosecx+cotx)=(cosec^2x-cot^2x)/(cosecx+cotx)=1/(cosecx+cotx)=(sinx)/(1+cosx)#
So,
#l=lim_(x to0)(cosecx-cotx)/x=lim_(x to0)(sinx)/(x(1+cosx)#
#l=lim_(x to0)sinx/x*lim_(x to0)1/(1+cosx)=(1)(1/(1+cos0))=1/2#

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