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Question

Find all values of θ , between 0 & π, which satisfy the equation cosθcos2θcos3θ=14.

A
0.π8,π3,3π8,5π8,2π3,7π8,π
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B
π8,π3,3π8,5π8,2π3,7π8
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C
π8,π3,3π8,5π8,7π8
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D
0,π8,3π8,5π8,7π8,π
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Solution

The correct option is B π8,π3,3π8,5π8,2π3,7π8
cosxcos2xcos3x=14
3cos2x10cos4x+8cos6x=14
Substitute y=cos2x
8y310y2+3y=14
(4y1)(8y28y+1)=0
y=14y=12±122
cos2x=14 or cos2x=12±122
x=π8,π3,3π8,5π8,2π3,7π8

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