Question

√200*cos²5π8-√50 выручите пожалуйста

Answer 1

$sqrt{200}* cos^{2} frac{ pi }{8} - sqrt{50} = sqrt{50}*( sqrt{4}* cos^{2} frac{5 pi }{8} -1) = sqrt{50} *(2cos^{2} frac{5 pi }{8}-1 )$
$= sqrt{25*2} *cos(2* frac{5 pi }{8} )=5 sqrt{2} *cos frac{5 pi }{4} =5 sqrt{2} *cos( pi + frac{ pi }{4} )=$
$=5 sqrt{2} *(-cos frac{ pi }{4} )=5 sqrt{2} *(- frac{ sqrt{2} }{2} )=-5$