√300 *cos²17π/12 -√75 = √(100*3) *cos²17π/12 -√(25*3) =
10√3 *(1 +cos 2*17π/12) /2 - 5√3 =5√3 + 5√3*cos(17π/6) - 5√3 =
5√3*cos(3π - π/6) = 5√3 *( -cosπ/6) = 5√3* (√3 /2 ) =15/2 =7,5.
* * * *
!!! cos²α =(1+cos2α) / 2 и cos(k*π -α) = - cosα , если k нечетное число.
cos(k*π -α) =cos( (2m-1)π -α) =cos(2πm -(π +α) )=cos(π +α) = - cosα.
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cos(3π - π/6) =cos(2π +π - π/6) = cos(π - π/6)= - cos π/6 = - √3 / 2.