The value of cos4π8+cos43π8+cos45π8+cos47π8 is
0
12
32
1
Explanation for correct option
Given trigonometric function is cos4π8+cos43π8+cos45π8+cos47π8
Therefore,
cos4π8+cos43π8+cos45π8+cos47π8=cos4π8+cos43π8+cos4π-3π8+cos4π-π8=cos4π8+cos43π8+cos4π8+cos43π8=2cos4π8+cos43π8=2cos4π8+cos4π2-π8=2cos4π8+sin4π8=2cos2π8+sin2π82-2cos2π8sin2π8∵a2+b2=a+b2-2ab=212-122.2cos2π8sin2π8=21-122cosπ8sinπ82=21-12sinπ42∵sin2A=2sinAcosA=21-12·12∵sinπ4=12=32
Hence, the correct option is OptionC