Sum of Trigonometric Ratios in Terms of Their Product
Period of c...
Question
Period of cosxcos(600−x)cos(600+x) is
A
π2
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B
π3
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C
2π3
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D
π
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Solution
The correct option is C2π3 Let f(x)=cosxcos(60o−x)cos(60o+x) =cosx[cos(120)+cos2x2][2cosAcosB=cos(A+B)+cos(A−B)] =cosx[cos2x−122] =cosx[2cos2x−14] =cosx[4cos2x−34][cos2x=2cos2x−1] =4cos3x−3cosx4 f(x)=cos3x4=coskx4 Period of f(x)=2π|k|=2π3