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Question

The number of distinct real roots of ∣ ∣sin xcos xcos xcos xsin xcos xcos xcos xsin x∣ ∣=0

in the interval π4xπ4 is

A
0 (zero)
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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 C 1
∣ ∣sin xcos xcos xcos xsin xcos xcos xcos xsin x∣ ∣=0

cos3x∣ ∣tan x111tan x111tan x∣ ∣=0

cos3x(tanx1)2(tanx+2)=0
cosx=0,tanx=1,tanx=2

cosx0 for any x[π4,π4]
and tanx2 for any x[π4,π4]

Thus, it has only one solution x=π4 in the given interval.

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