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Question

Exhaustive set to values of x satisfying |cos3x+sin3x|=|cos3x|+|sin3x| in [0,π2] is :

A
[0,π6]
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B
[0,π2]
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C
[0,π2](π6,π3)
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D
[0,π2](π4,π3)
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Solution

The correct option is C [0,π2](π6,π3)
sin3x+cos3x=sin3x+cos3x
we know, a+b=a+b is only true if ,
ab0
sin3x.cos3x0sin6x0
thus solution in the given interval is,
6x[0,π][2π,3π]

x[0,π3][π3,π2]=[0,π2](π6,π3)
Hence, option 'C' is correct.

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