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Question


The smallest positive x satisfying logcosxsinx+logsinxcosx=2 is

A
π2
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B
π3
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C
π4
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D
π6
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Solution

The correct option is C π4

using base change formula we get
log(sinx)log(cosx)+log(cosx)log(sinx)=2
this gives log(sinx)log(cosx)=1
so sinx=cosx
smallest x satisfying this is Π4


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