Period of cosx·cos(60°-x)·cos(60°+x) is:
π2
π
π3
2π3
The explanation for the correct option.
Let,
f(x)=cosx·cos(60°-x)·cos(60°+x)⇒=cosxcos120°+cos2x2[∵2cosAcosB=cos(A+B)+cos(A-B)]⇒=cosxcos2x-122[∵cos120°=-12]⇒=cosx2cos2x-14⇒=cosx2(2cos2x-1)-14[∵cos2x=2cos2x-1]⇒=cosx4cos2x-34⇒=4cos3x-3cosx4⇒=cos3x4[∵cos3x=4cos3x-3cosx]
Compare f(x)=cos3x4 from coskx4, We get k=3.
∴Period=2πk=2π3
Hence, the option D is correct.