Question

$sqrt{32}cos^{2}frac{13pi}{8}-sqrt{32}sin^{2}frac{13pi}{8}$

Answer 1

$sqrt{32}cos^{2}frac{13pi}{8}-sqrt{32}sin^{2}frac{13pi}{8}=sqrt{32}(cos^{2}frac{13pi}{8}-sin^{2}frac{13pi}{8})=\ \ =sqrt{32}*cos(2*frac{13pi}{8})=sqrt{32}*cosfrac{13pi}{4}=sqrt{32}*cos(frac{8pi}{4}+frac{5pi}{4})=\ \ =sqrt{32}*cos(2pi+frac{5pi}{4})=sqrt{32}*cosfrac{5pi}{4}=sqrt{32}*cos(frac{4pi}{4}+frac{pi}{4})=\ \ =sqrt{32}*cos(pi+frac{pi}{4})=-sqrt{32}*cosfrac{pi}{4}=-sqrt{32}*frac{sqrt{2}}{2}=\ \ =-frac{sqrt{64}}{2}=-frac{8}{2}=-4$