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Question

Let f(x) be a non-negative function. If f(x)cosxf(x)sinx,x0, then value of f(5π3) is

A
1
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B
12
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C
0
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D
32
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Solution

The correct option is C 0
f(x)cosxf(x)sinx
f(x)cosxf(x)sinx0
ddx(f(x)cosx)0

g(x)=f(x)cosx is decreasing x0
g(x)g(0)
f(x)cosxf(0)cos0
f(x)cosxf(0)

We know that
5π3π2
g(5π3)g(π2) (g(x) is decreasing)
g(5π3)0 [g(π2)=0]
f(5π3)×cos(5π3)0
f(5π3)×cos(π3)0
f(5π3)0

but f(x)0 (Given in the question)

So, f(5π3)=0

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