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Question

If x=sin1+cos1,y=sin1+cos1 and z=sin1cos1, then which among the following relation between x,y,z is correct ?

A
x>y>z
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B
y>x>z
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C
z>x>y
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D
z>y>x
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Solution

The correct option is B y>x>z
We know that, 1 radian5718(0,π2)
So, sin1>sin1>0 and cos1>cos1>0
As sinx and cosx are positive and proper fractions in x(0,π2)

sin1+cos1>sin1+cos1
y>x ...(i)

Also,
sin1+cos1>sin1cos1(cos1>0)
x>z ...(ii)

From (i) and (ii)
y>x>z



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