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Question

Evaluate limx0sin(1+x)sin(1x)x

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Solution

limx0sin(1+x)sin(1x)x

Using sinCsinD=2sin(CD2)cos(C+D2)

limx02sin((1+x)(1x)2)cos((1+x)+(1x)2)x

limx02cos1sinxx=2cos1

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