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Question

limx0xtan2x2xtanx(1cos2x)2 equal ?

A
14
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B
1
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C
12
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D
12
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Solution

The correct option is C 12
limx0xtan(2x)2xtanx(1cos2x)2
=limxto0xtan(2x)2xtanx(2sin2x)2
=14limx0xtan2x2xtanxsin2x
=14limxto0tan2x2tanxsin3x
=14limxto02tanx1tanx2tanxsin3x
=14limx02tanx2tanx+2tan3x(1tan2x)(sin3x)
=14limx021tan2x×limx0(tanxsinx)3
=14×210×1
=12

1056919_1152009_ans_d2300d24367a4c0fa8255181cf28e19a.jpg

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