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Question

Evaluate: limx0sin2x+2sin2x2sinxcosxcos2x

A
0
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B
1
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C
23
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D
4
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Solution

The correct option is D 4
limx0sin2x+2sin2x2sinxcosxcos2x

=limx02sinxcosx+22cos2x2sinxcosxcos2x
=2limx0sinxcosxsinx(cos2x1)cosxcos2x
=2.limx0sinx(cosx1)(cosx1)(cosx+1)cosxcos2x
=2.limx0(cosx1)(sinxcosx1)cosx(1cosx)
=2.limx01sinx+cosxcosx=2×2=4

Hence option D is the answer.

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