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Question

Evaluate :
limx0xln(1+2tanx)1cosx

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Solution

limx0xln(1+2tanx)1cosx
=limx0xln(1+2tanx)(1cosx)×2tanx× 2tanx
=limx0x×2tanx1cosx
=limx0x.2.tanxx.x2sin2x2
=limx0x2sin2x2
=limx04(x2)2sin2x2
=4.

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