Question

$sqrt{72} * cos^{2} frac{15 pi }{8} - sqrt{18}$

Answer 1

$sqrt{71}cdot cos^2frac{15pi}{8}-sqrt{18}=sqrt{72}cdot cos^2(2pi -frac{pi}{8})-sqrt{18}=\\=sqrt{72}cdot cos^2frac{pi}{8}-sqrt{18}=sqrt{4cdot 18}cdot frac{1+cosfrac{2pi}{8}}{2}-sqrt{18}=$

$=2sqrt{18}cdot frac{1+cosfrac{pi}{4}}{2}-sqrt{18}=sqrt{18}cdot (1+frac{sqrt2}{2})-sqrt{18}=\\=sqrt{9cdot 2}cdot frac{2+sqrt2}{2}-sqrt{9cdot 2}=3sqrt2cdot (frac{2+sqrt2}{2}-1)=\\=3sqrt2cdot frac{2+sqrt2-2}{2}=3sqrt2cdot frac{sqrt2}{2}=3$