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Question

The value of cos3π8cos3π8+sin3π8sin3π8 is :

A
14
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B
122
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C
12
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D
12
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Solution

The correct option is B 122
cos3π8cos3π8+sin3π8sin3π8

=cos3π8[4cos3π83cosπ8]+sin3π8[3sinπ84sin3π8]

=4[cos6π8sin6π8]+3[sin4π8cos4π8]

=4[cos2π8sin2π8][cos4π8+sin4π8+cos2π8sin2π8]3[cos2π8sin2π8]

=[cos2π8sin2π8][4(1cos2π8sin2π8)3]
=cosπ4[1sin2π4]=122

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