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Question

lf sin4x+cos4y+2=
4 sinxcosy,0<x,y≤π2 , then sinx+cosy equal to

A
0
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B
2
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C
1
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D
2
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Solution

The correct option is B 2

apply AM-GM for sin4x,cos4y,1,1
we get sin4x+cos4y+1+14>(sin4xcos4y)14
this gives sin4x+cos4y+2>4sinxcosy
here as given , equality occurs
so sinx=cosy=1
so sinx+cosy=2


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