Question

Найдите значение выражения

Answer 1

$sqrt{27} * cos^{2} frac{13 pi }{12} - sqrt{27} * sin^{2} frac{13 pi }{12} = sqrt{27} *(cos ^{2} frac{13 pi }{12} - sin^{2} frac{13 pi }{12} )=$
$= sqrt{27} *cos(2* frac{13 pi }{12} )= sqrt{27} *cos frac{26 pi }{12} = sqrt{27}*cos( frac{24 pi }{12} + frac{2 pi }{12} )=$
$= sqrt{27} *cos(2 pi + frac{ pi }{6} )= sqrt{27}*cos frac{ pi }{6} = sqrt{27}* frac{ sqrt{3} }{2} = frac{9}{2}=4,5$