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How demonstrate cos x < cos(x/3)cos(2x/3), given x>0, x<`pi` ?
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High School Teacher
Prove that `cosx<cos(x/3)cos((2x)/3)` for `0<x<pi` :
Note that on `0<x<pi` `sinx>0`
`cosx=cos(x/3+(2x)/3)` (Since `x/3+(2x)/3=x` )
`=cos( x/3)cos ((2x)/3)-sin (x/3)sin ((2x)/3)`
`<cos(x/3)cos((2x)/3)` as required.
(We are subtracting a positive number)
Posted by embizze on October 3, 2012 at 1:46 AM (Answer #1)
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