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Question

limxπ4cot3xtanxcos(x+π4) is:

A
42
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B
4
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C
82
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D
8
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Solution

The correct option is D 8
limxπ4cot3xtanxcos(x+π4)=limxπ41tan4xtan3x(12cosx12sinx)=limxπ4(1+tan2x)(1tan2x)12tan3x.(cosxsinx)=2limxπ4(1+1).(cos2xsin2x).cos3xsin3x.cos2x.(cosxsinx)=22limxπ4(cosx+sinx)(cosxsinx).cosxsin3x.(cosxsinx)=22.(12+12)12(12)3=22221=8

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