Question

Найдите значение выражения $\sqrt{72} cos^{2} \frac{5 \pi }{8} - \sqrt{18}$

Answer 1

$cos^2 \frac{5 \pi }{8} =cos^2( \frac{ \pi }{2} + \frac{ \pi }{8} )=sin^2\frac{ \pi }{8}$
$sin^2\frac{ \pi }{8}= \frac{1-cos \frac{ \pi }{4} }{2} \frac{1- \frac{ \sqrt{2} }{2} }{2} = \frac{2- \sqrt{2} }{4}$
$\sqrt{72} *\frac{2- \sqrt{2} }{4} - \sqrt{18} = \frac{6 \sqrt{2}*(2- \sqrt{2}) }{4} -3 \sqrt{2} = \frac{12 \sqrt{2}-12-12 \sqrt{2} }{4} = \frac{-12}{4} =-3$