Question

Найдите значение выражения:
1)$sqrt{32}cos^2 frac{ pi }{8}- sqrt{8}$
2)$sqrt{75}cos^2 frac{7 pi }{12}- sqrt{75}sin^2 frac{7 pi }{12}$
3)$sqrt{48}- sqrt{192} sin^2 frac{19 pi }{12}$

Answer 1

1)4√2*(1+сosπ/4)/2 -2√2=2√2(1+√2/2)-2√2=2√2+2-2√2=2
2)5√3*(cos²7π/12-sin²7π/12)=5√3*cos7π/6=5√3cos(π+π/6)=-5√3cosπ/6=-5√3*√3/2=
=-7,5
3)4√3-8√3sin²19π/12=4√3(1-2sin²19π/12)=4√3cos19π/6=4√3cos(3π+π/6)=
=-4√3cosπ/6=-4√3*√3/2=-6