logcosx=log(1+cosx-1)which can be expanded using expansion of ln(1+x)=x-x^2/2---------------
x^/2 are neglected as they would always tend to zero.
hence ln(1+cosx-1)can be simply written as=(cosx-1)
therefore limit simplifies to:
Lt (cosx-1)/x^2which is -1/2..........
Hope you understand......
(i have used some rule which are simple to prove and can be used to simplify calculation)
rules: [ x][0 ] sinx tends to x
rule :[t ][ o] ln(1+t) tends to t
here x tend to 0 so x2 tends to 0 so simply replace ln(1-x2/2) by -x2/2
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