Maximum value of `|costhetacos(60^0-theta)cos(60^0+theta)` for all values of `thetadot`

Options

A. 1/2
B. 1/4
C. 1/8
D. None of these

Answer

B

Explanation

Let `{f}({x})=cos {x} cos (60^{circ}-{x}) cos (60^{circ}+{x}) `

`=cos {x}[frac{cos (120)+cos 2 {x}}{2}][2 cos {A} cos {B}=cos ({A}+{B})+cos ({A}-{B})] `

`=cos {x}[frac{cos 2 {x}-frac{1}{2}}{2}] `

`=cos {x}[frac{2 cos 2 {x}-1}{4}] `

`=cos {x}[frac{4 cos ^{2} {x}-3}{4}][cos 2 {x}=2 cos ^{2} {x}-1] `

`=frac{4 cos 3 {x}-3 cos {x}}{4} `

`{f}({x})=frac{cos 3 {x}}{4}=frac{cos {kx}}{4} `

Period of `{f}({x})=frac{2 pi}{|{k}|}=frac{2 pi}{3}`