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Question

The value of limx0(1+tanx1+sinx)1/sinx is

A
1
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1
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C
0
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Solution

The correct option is A 1
Let, L=limx0(1+tanx1+sinx)1/sinx

Clearly form of the limit is 1, So

L=limx0(1+1+tanx1+sinx1)1/sinx

=limx0(1+tanxsinx1+sinx)1+sinxtanxsinx.tanxsinx(1+sinx)sinx

=elimx0tanxsinx(1+sinx)sinx

=elimx0tanxxsinxx(1+sinx)sinxx=e11=e0=1

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