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Question

1+cosπ81+cos3π81+cos5π81+cos7π8


A

12

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B

14

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C

18

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D

116

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Solution

The correct option is C

18


Explanation for the correct option:

Step 1. Solve the given expression:

1+cosπ81+cos3π81+cos5π81+cos7π8

=1+cosπ81+cos3π81+cosπ-3π81+cosπ-π8

=1+cosπ81+cos3π81-cos3π81-cosπ8 cos(π-θ)=-cosθ

=1+cos2π81+cos23π8

=sin2π81-cos2π2-π8

=sin2π8cos2π8 1-cos2(π2-θ)=cos2θ

Step 2. Multiply and divide it by 4:

=14×2sinπ8cosπ82sinπ8cosπ8

=14×sinπ4sinπ4 2sinθcosθ=sin2θ

=14×sin2π4

=14×122=18 sinπ4=12

Hence, Option ‘C' is Correct.


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