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Question

The value of cosπ15·cos2π15·cos4π15·cos8π15 is


A

116

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B

-116

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C

1

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D

0

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Solution

The correct option is B

-116


Explanation for correct option

Given trigonometric function is cosπ15·cos2π15·cos4π15·cos8π15

cosπ15·cos2π15·cos4π15·cos8π15=cosπ15·cos4π15·cos2π15·cos8π15=142cosπ15·cos4π15·2cos2π15·cos8π15=14cos4π15+π15+cos4π15-π15·cos8π15+2π15+cos8π15-2π152cosacosb=cosb+a+cosb-a=14cosπ3+cosπ5·cos2π3+cos2π5=1412+5+14·-12+5-14cosπ3=12,cos2π3=-12,cos2π5=5-14andcosπ5=5+14=145+34·5-34=145-916a2-b2=a+ba-b=-116

Hence, the correct option is optionB


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